Question

What is the measure of angle D if angle F is 110 and angle E is 100?

Answer 1

F, E and D are exterior angles.

Exterior angles and corresponding interior angles are suppementary (they add up to 180°)

Use F to find the meaure of C:

`\begin{gathered} F+C=180 \\ C=180-F \\ C=180-110 \\ C=70 \end{gathered}`

Use E to find the measure of B:

`\begin{gathered} E+B=180 \\ B=180-E \\ B=180-100 \\ B=80 \end{gathered}`

The sum of the interiror angles of any triangle is 180°.

Use B and C to find the meaure of A:

`\begin{gathered} A+B+C=180 \\ A=180-B-C \\ A=180-80-70 \\ A=30 \end{gathered}`

Use A to find the meaure of D:

`\begin{gathered} A+D=180 \\ D=180-A \\ D=180-30 \\ D=150 \end{gathered}`Then, the measure of angle D is 150°