Question

It says solve for the unknown, then find the measure of the angle given

Answer 1

The Solution:

Given:

In both figures, we are asked to find the unknown and the given angles.

Question(9):

By the Alternate Angles theorem,

$\begin{gathered} (a+28)^o=2a^o \\ a+28=2a \end{gathered}$

Subtract a from both sides, we get

$\begin{gathered} a-a+28=2a-a \\ 28=a \\ a=28 \end{gathered}$

To find angle MNP.

Substitute 28 for a in (a+28).

$\angle MNP=a+28=28+28=56^o$

Thus, the correct answers are:

$\begin{gathered} a=28 \\ \angle MNP=56^o \end{gathered}$

Question (10):

Again, by the Alternate Angles theorem,

$\begin{gathered} 5y=2y+78 \\ Subtracting\text{ 2y from both sides, we get} \\ 5y-2y=2y-2y+78 \\ 3y=78 \end{gathered}$

Dividing both sides by 3, we get

$\begin{gathered} y=\frac{78}{3}=26 \\ y=26 \end{gathered}$

Now, find angle WXZ.

$\angle WXZ=5y=5\times26=130^o$

Therefore, the correct answers are:

$\begin{gathered} y=26 \\ \angle WXZ=130^o \end{gathered}$