Q. If a triangle has angles of 50 degrees and 60 degrees, what is the measure of the third angle?
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A.
70 degrees
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B.
80 degrees
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C.
90 degrees
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D.
100 degrees
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 50 - 60 = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. If the radius of a circle is 5 cm, what is the circumference of the circle?
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A.
10π cm
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B.
15π cm
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C.
20π cm
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D.
25π cm
Solution
The circumference of a circle is given by the formula C = 2πr. Thus, C = 2π(5) = 10π cm.
Correct Answer:
A
— 10π cm
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Q. If two angles are corresponding angles formed by a transversal intersecting two parallel lines, what is their relationship?
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A.
They are equal.
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B.
They are complementary.
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C.
They are supplementary.
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D.
They are not related.
Solution
Corresponding angles are equal when a transversal intersects two parallel lines.
Correct Answer:
A
— They are equal.
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Q. If two angles are supplementary and one angle measures 35 degrees, what is the measure of the other angle?
-
A.
145 degrees
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B.
35 degrees
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C.
90 degrees
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D.
55 degrees
Solution
Supplementary angles sum to 180 degrees, so the other angle is 180 - 35 = 145 degrees.
Correct Answer:
A
— 145 degrees
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Q. If two lines are parallel and a transversal intersects them, what is the sum of the interior angles on the same side of the transversal?
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A.
90 degrees
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B.
180 degrees
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C.
360 degrees
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D.
It varies.
Solution
The sum of the interior angles on the same side of the transversal is 180 degrees.
Correct Answer:
B
— 180 degrees
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Q. If two lines are parallel, what can be said about the corresponding angles formed by a transversal?
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A.
They are equal.
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B.
They are complementary.
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C.
They are supplementary.
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D.
They are different.
Solution
Corresponding angles formed by a transversal with parallel lines are equal.
Correct Answer:
A
— They are equal.
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Q. In a circle, if two chords intersect at a point inside the circle, how do you find the measure of the angles formed?
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A.
Add the angles.
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B.
Subtract the angles.
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C.
Multiply the angles.
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D.
Average the angles.
Solution
The measure of each angle formed is equal to the sum of the measures of the arcs intercepted by the angle.
Correct Answer:
A
— Add the angles.
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Q. In a right triangle, if one angle measures 30 degrees, what is the measure of the angle opposite the shortest side?
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A.
30 degrees
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B.
60 degrees
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C.
90 degrees
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D.
45 degrees
Solution
In a right triangle, the angle opposite the shortest side is the smallest angle, which is 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In coordinate geometry, what is the slope of a line that is parallel to the line represented by the equation y = 3x + 2?
Solution
Parallel lines have the same slope. The slope of the given line is 3.
Correct Answer:
A
— 3
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Q. In coordinate geometry, what is the slope of a line that passes through the points (2, 3) and (4, 7)?
Solution
The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2.
Correct Answer:
A
— 2
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Q. Two lines are parallel, and a transversal intersects them, creating angles of 75 degrees and x degrees. What is the value of x?
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A.
75 degrees
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B.
105 degrees
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C.
180 degrees
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D.
90 degrees
Solution
The angles are supplementary, so x = 180 - 75 = 105 degrees.
Correct Answer:
B
— 105 degrees
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Q. What is the circumference of a circle with a diameter of 10 cm?
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A.
31.4 cm
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B.
20 cm
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C.
15.7 cm
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D.
25 cm
Solution
The circumference of a circle is calculated using the formula C = πd. For d = 10 cm, C = π(10) ≈ 31.4 cm.
Correct Answer:
A
— 31.4 cm
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Q. What is the measure of an angle formed by a tangent and a chord drawn from the point of contact?
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A.
It is equal to the angle subtended by the chord at the center.
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B.
It is equal to half the angle subtended by the chord at the circumference.
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C.
It is equal to the angle subtended by the tangent at the center.
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D.
It is always 90 degrees.
Solution
The angle formed by a tangent and a chord is equal to half the angle subtended by the chord at the circumference.
Correct Answer:
B
— It is equal to half the angle subtended by the chord at the circumference.
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Q. What is the relationship between the angles formed by two intersecting lines?
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A.
They are equal.
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B.
They are complementary.
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C.
They are supplementary.
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D.
They are not related.
Solution
The angles formed by two intersecting lines are supplementary, meaning they add up to 180 degrees.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the angles formed by two parallel lines cut by a transversal?
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A.
All angles are equal.
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B.
Corresponding angles are equal.
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C.
Alternate exterior angles are equal.
-
D.
Both B and C.
Solution
Corresponding angles and alternate exterior angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
D
— Both B and C.
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