Question

the Question asks: calculate the measure of each lettered angle. Congruent angles and right angles are indicated.I didn't know what steps to take to find the lettered angles. how do I find the lettered angles?

Answer 1

Let's find the lettered angles:

To find the angles seperate the traingles, and solve for each using the Triangle Angle Sum theorem.

$\begin{gathered} m\angle a=180-90=\frac{90}{2}=45\degree \\ \\ \end{gathered}$$\begin{gathered} m\angle d=180-80-20=80\degree \\ \\ m\angle d=80\degree \end{gathered}$$\begin{gathered} m\angle f=180-65-45=70\degree \\ \\ m\angle f=70\degree \end{gathered}$$\begin{gathered} m\angle g=90-70=20\degree \\ \\ m\angle g=20\degree \end{gathered}$$\begin{gathered} 180-45-20=115 \\ \\ m\angle b=180-20-115=45 \\ \\ m\angle b=45\degree \end{gathered}$$\begin{gathered} m\angle h=180-80-45=55 \\ \\ m\angle h=55\degree \end{gathered}$$\begin{gathered} 180-95-55=30 \\ \\ m\angle c=180-(30+20) \\ \text{ =180-50 = 130}=\frac{130}{2}=65 \\ \text{ } \\ m\angle c=65\degree \end{gathered}$$\begin{gathered} 180-95=85 \\ \\ m\angle e=180-65-85=30 \\ \\ m\angle e=30\degree \end{gathered}$

ANSWER:

$\begin{gathered} m\angle a=45\degree \\ \\ m\angle b=45\degree \\ \\ m\angle c=65\degree \\ \\ m\angle d=80\degree \\ \\ m\angle e=30\degree \\ \\ m\angle f=70\degree \\ \\ m\angle g=20\degree \\ \end{gathered}$