Question

Find the following, when a = 30°, b = 54°, c = 49°, and d = 82°. Find measure MYN and measure MXZ

Answer 1

(a)m∠MYN=47°

(b)m∠MXZ=14°

Explanation:

The given angles in the diagram are labeled below.

The sum of the measures of angles in a triangle is 180 degrees.

(a)In triangle XYN

`\begin{gathered} a+b+m\angle\text{MYN}+c=180\degree \\ 30\degree+54\degree+m\angle\text{MYN}+49\degree=180\degree \\ m\angle\text{MYN}+133\degree=180\degree \\ m\angle\text{MYN}=180\degree-133\degree \\ m\angle\text{MYN}=47\degree \end{gathered}`

(b)In triangle XYZ

`\begin{gathered} a+b+m\angle\text{MXZ}+d=180\degree \\ 30\degree+54\degree+m\angle\text{MXZ}+82\degree=180\degree \\ m\angle\text{MXZ}+166\degree=180\degree \\ m\angle\text{MXZ}=180\degree-166\degree \\ m\angle\text{MXZ}=14\degree \end{gathered}`