Angles and Parallel Lines - Problems on Triangles

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Q1. 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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Q2. In triangle DEF, if angle D = 30° and angle E = 45°, what is angle F?

Solution:

Angle F = 180° - (30° + 45°) = 105°.

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Q3. What is the measure of each angle in an equilateral triangle?

Solution:

In an equilateral triangle, each angle measures 60°.

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Q4. 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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Q5. In triangle JKL, if angle J = 90° and angle K = 45°, what is the measure of angle L?

Solution:

In a right triangle, the sum of the angles is 180°. Therefore, angle L = 180° - (90° + 45°) = 45°.

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Q6. In triangle GHI, if angle G = 30° and angle H = 70°, what is the measure of angle I?

Solution:

The sum of angles in a triangle is 180°. Therefore, angle I = 180° - (30° + 70°) = 80°.

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Q7. 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°.

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Q8. 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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Q9. In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?

Solution:

Using the sine rule: g/h = sin(G)/sin(H) => g/10 = sin(30°)/sin(60°) => g = 10 * (1/2) / (√3/2) = 10/√3 = 8.66.

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Q10. 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.