Question

∠X and ∠Y are a pair of supplementary angles. The measure of ∠Y is three times the measure of ∠X. Which of these gives the measures of ∠X and ∠Y?

Answer 1

The measure of the angles are ∠X = 45° , ∠Y = 135° [ The correct option is D. 45° and 135° ]

Correct question : ∠X and ∠Y are a pair of supplementary angles. The measure of ∠Y is three times the measure of ∠X. Which of these gives the measures of ∠X and ∠Y? A. 22.5° and 67.5° B. 18° and 72° C. 36° and 144° D. 45° and 135°

Given :

∠X and ∠Y are a pair of supplementary angles. The measure of ∠Y is three times the measure of ∠X.

To find :

Which of these gives the measures of ∠X and ∠Y

A. 22.5° and 67.5°

B. 18° and 72°

C. 36° and 144°

D. 45° and 135°

Solution :

Step 1 of 2 :

Form the equation to find measures of ∠X and ∠Y

The measure of ∠Y is three times the measure of ∠X.

∴ ∠Y = 3∠X

Here it is given that ∠X and ∠Y are a pair of supplementary angles

We know that two angles are said to be supplementary if sum of the angles is 180°

So by the given condition

∠X + ∠Y = 180°

⇒ ∠X + 3∠X = 180°

Step 2 of 2 :

Calculate measures of ∠X and ∠Y

∠X + 3∠X = 180°

⇒ 4∠X = 180°

⇒ ∠X = 180°/4

⇒ ∠X = 45°

∴ ∠Y = 3∠X = 3 × 45° = 135°

So measure of the angles are ∠X = 45° , ∠Y = 135°

Hence the correct option is D. 45° and 135°

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