Question

5 What is the measure of ZA? B 53 X 105° C A

Answer 1

We are asked to find the measure of ∠A

First, we have to find the measure of ∠C

Recall the straight-line angle property

`\angle C+105\degree=180\degree`

Let us solve for angle ∠C

`\begin{gathered} \angle C+105\degree=180\degree \\ \angle C=180\degree-105\degree \\ \angle C=75\degree \end{gathered}`

Now recall that the sum of all three angles of a triangle must be equal to 180°

`x+53\degree+75\degree=180\degree`

Let us solve for angle x

`\begin{gathered} x+53\degree+75\degree=180\degree \\ x=180\degree-53\degree-75\degree \\ x=52\degree \end{gathered}`

Therefore, the measure of ∠A is 52°