Question

directions: find the value of each variable
3.
ef =

m∠f =

directions: find each missing measure.
1.

m∠t =

m∠u =

2.

m∠m =

m∠n =

4.

m∠p =

m∠q =

m∠r =

Explanation:

Step1: Use triangle angle - sum property

The sum of interior angles of a triangle is \(180^{\circ}\).

Step2: Analyze triangle \(EFG\)

In \(\triangle EFG\), \(\angle E=\angle G = 23^{\circ}\). Let \(\angle F=x\). Then \(x + 23^{\circ}+23^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(23^{\circ}+23^{\circ})=134^{\circ}$$

Since \(\triangle EFG\) has two equal angles (\(\angle E=\angle G\)), it is an isosceles triangle. So \(EF = FG\). Given \(FG = 18\) in, so \(EF=18\) in.

Answer:

\(m\angle F = 134^{\circ}\), \(EF = 18\) in