Angles and Parallel Lines - Problems on Triangles

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Q1. What is the measure of each angle in an equilateral triangle?

Solution:

In an equilateral triangle, each angle measures 60°.

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Q2. In triangle ABC, if angle A = 50° and angle B = 60°, what is the measure of angle C?

Solution:

The sum of angles in a triangle is 180°. Therefore, angle C = 180° - (50° + 60°) = 70°.

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Q3. In triangle JKL, if angle J = 80° and angle K = 50°, what is angle L?

Solution:

Angle L = 180° - (80° + 50°) = 50°.

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Q4. If two angles are vertical angles and one angle measures 120°, what is the measure of the other angle?

Solution:

Vertical angles are equal, so the other angle also measures 120°.

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Q5. If two parallel lines are cut by a transversal and one of the corresponding angles is 75°, what is the measure of the other corresponding angle?

Solution:

Corresponding angles are equal when two parallel lines are cut by a transversal.

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Q6. If angle X and angle Y are complementary and angle X measures 35°, what is the measure of angle Y?

Solution:

Complementary angles sum to 90°. Therefore, angle Y = 90° - 35° = 55°.

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Q7. What is the relationship between the exterior angle of a triangle and the two opposite interior angles?

Solution:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

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Q8. If two lines are parallel and a transversal intersects them, what can be said about the corresponding angles?

Solution:

Corresponding angles are equal when two parallel lines are cut by a transversal.

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Q9. If two angles are supplementary and one angle measures 3x and the other measures 2x, what is the value of x?

Solution:

3x + 2x = 180°. Therefore, 5x = 180°; x = 36°. The question asks for x, which is 15.

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Q10. In triangle GHI, if angle G = 70° and angle H = 40°, what is the measure of angle I?

Solution:

Angle I = 180° - (70° + 40°) = 70°.