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

Given angles

(2x — 1)° and (x + 4)°

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

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

(2x — 1)° + (x + 4)° = 180°

Combine x terms and find the value of x

⇒ 2x - 1 + x + 4 = 180

⇒ 3x + 3 = 180

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

⇒ 3x = 180 - 3

⇒ 3x = 177

⇒ x = \$177/3\$

⇒ x = 59

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

First angle

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

Second angle

\$(x + 4)° = (59 + 4)° = 63°\$

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

Can you summarize what you’ve understood in the above steps?

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

117°, 63°

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

30°, 45°

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

35°, 55°

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

40°, 55°

Option

A

Can you summarize what you’ve understood in the above steps?