1

Problem

If angles of measures (2x - 1)° and (x + 4)° are a pair of supplementary angles. Find the measures.

2

Step

GIven angles

(2x - 1)° and (x + 4)°

3

Hint

Supplementary angles are defined as two angles whose sum equals 180°.

4

Step

So, we can set up the equation for the given pair of supplementary angles:

(2x - 1)° + (x + 4)° = 180°

5

Step

Combine x terms and find the value of x:

2x - 1 + x + 4 = 180

3x + 3 = 180

6

Step

Subtract 3 from each side of the equation and divide the result by 3:

3x = 180 - 3

3x = 177

x = \$(177)/3 = 59\$

7

Hint

Now that we have the value of x, we can find the measures of the two angles:

8

Step

First angle:

(2x - 1)° = (2 \$\times\$ 59 - 1)° = 117°

9

Step

Second angle:

(x + 4)° = (59 + 4)° = 63°

10

Solution

So, the measures of the two angles are 117° and 63°, and they form a pair of supplementary angles.

11

Sumup

Please summarize steps

Choices

12

Choice-A

It is the correct answer. 117°, 63°, as the angles satisfy the condition of being supplementary (adding up to 180°)

Correct 117°, 63°

13

Choice-B

Substituting x = 30 gives us 59° and 34°. As they don’t add up to 180°, option B is incorrect

Wrong 30°, 45°

14

Choice-C

Substituting x = 35 gives us 69° and 39°. As they don’t add up to 180°, option B is incorrect

Wrong 35°, 55°

15

Choice-D

Substituting x = 40 gives us 79° and 44°. As they don’t add up to 180°, option B is incorrect

Wrong 40°, 55°

16

Answer

Option

A

17

Sumup

Please summarize choices