Question

select the correct answer. in the figure, angle g measures 102° and angle d measures 30°. what is the measurement of angle b. 24°, 42°, 60°,or 102°

Answer 1

Notice that angles G and the third angle (let's call it x) from triangle ABX lay in the same straight line.

This way,

`\begin{gathered} x+G=180\rightarrow x=180-G \\ \Rightarrow x=78 \end{gathered}`

Now, we know that angles A and D add up to 90°. This way,

`\begin{gathered} A+D=90 \\ \rightarrow A=90-D \\ \rightarrow A=60 \end{gathered}`

We also know that the sum of the interior angles of a triangle is 180.

Therefore,

`B+A+x=180`

Solving for B we get:

`\begin{gathered} B=180-A-x \\ \Rightarrow B=42 \end{gathered}`

Angle B measures 42°.

Answer: B. 42°