Use the given information to determine the measures of the angles in each pair. 18. The measure of the complement of an angle is three times the measure of the angle. What is the measure of each angle? 19. The measure of the supplement of an angle is one fourth the measure of the angle. What is the measure of each angle? 20. Name each pair of vertical angles. 26 10 12 3 48 Identify the property demonstrated in each example. 21. GH = MN and MN = OP, so GH = OP 22. m1 = 134° and m/2 = 134°, so mZ1 = m/2 Substitution Property of equality 2

ignore the answer writien down on the last question unless its right.

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lexie2fine lexie2fine · Answer 1 · 2024-05-21T09:43:38-04:00

Answer: The measure of the complement of an angle is three times the measure of the angle.

Let the measure of the angle be x. Then, the measure of its complement is 3x.

We know that the sum of an angle and its complement is 90°:

x + 3x = 90°

Combine like terms:

4x = 90°

Divide by 4:

x = 22.5°

So, the measure of the angle is 22.5°, and the measure of its complement is 3(22.5°) = 67.5°.

The measure of the supplement of an angle is one fourth the measure of the angle.

Let the measure of the angle be x. Then, the measure of its supplement is x/4.

We know that the sum of an angle and its supplement is 180°:

x + x/4 = 180°

Combine like terms:

5x/4 = 180°

Multiply by 4/5:

x = 144°

So, the measure of the angle is 144°, and the measure of its supplement is 144°/4 = 36°.

Name each pair of vertical angles.

The pairs of vertical angles are:

∠26 and ∠10

∠12 and ∠3

∠48 and its corresponding vertical angle (not shown)

GH = MN and MN = OP, so GH = OP

This demonstrates the Transitive Property of Equality.

m∠1 = 134° and m∠2 = 134°, so m∠1 = m∠2

This demonstrates the Substitution Property of Equality.

Step-by-step explanation: