Question

ZA and ZB are supplementary angles. If m A = (5x + 25)° and mZB = (3x + 19)°, then find the measure of ZB.

Answer 1

We know that

• ZA and ZB are supplementary angles: This means their sum is equal to 180°.

Using the given information, we can express the following

`m\angle ZA+m\angle ZB=180`

Replacing the given expressions, we have

`5x+25+3x+19=180`

First, we reduce like terms

`8x+44=180`

Now, we subtract 44 on each side-

`\begin{gathered} 8x+44-44=180-44 \\ 8x=136 \end{gathered}`

Then, we divide the equation by 8

`\begin{gathered} (8x)/(8)=(136)/(8) \\ x=17 \end{gathered}`

We use this value to find the measure of angle ZB

`m\angle ZB=3x+19=3(17)+19=51+19=70`

Therefore, the measure of angle ZB is 70°