Question

question 5
quadrilateral efgh is an isosceles trapezoid with bases eh and fg. the measure of angle hgf is (7y + 6)°, and the measure of angle efg is (8y + 4)°. what is the measure of angle hgf?

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. So, $\angle HGF=\angle EFG$.
Set up the equation: $7y + 6=8y + 4$.

Step2: Solve the equation for y

Subtract $7y$ from both sides: $7y+6 - 7y=8y + 4-7y$.
We get $6=y + 4$.
Then subtract 4 from both sides: $6-4=y+4 - 4$.
So, $y = 2$.

Step3: Find the measure of $\angle HGF$

Substitute $y = 2$ into the expression for $\angle HGF$.
$\angle HGF=7y + 6=7\times2+6$.
$=14 + 6=20^{\circ}$.

Answer:

$20^{\circ}$