Question

Quadrilateral efgh is an isosceles trapezoid with bases eh and fg. the measure of angle hgf is (9y 3)°, and the measure of angle efg is (8y 5)°. what is the measure of angle hgf? trapezoid e f g h is drawn with parallel bases e h and f g.

a. 20°
b. 21°
c. 90°
d. 93°

Answer 1

The measure of angle HGF in the isosceles trapezoid is 93 degrees.

Step-by-step explanation:

In an isosceles trapezoid, the adjacent angles of each of the non-parallel sides (legs) are supplementary, meaning they add up to 180 degrees. With angle HGF being (9y + 3)° and angle EFG being (8y + 5)°, we can write the equation (9y + 3)° + (8y + 5)° = 180°. Combining like terms, we have 17y + 8 = 180. Subtracting 8 from both sides gives us 17y = 172, and dividing by 17 yields y = 10.1176, but since we are dealing with degrees, we should round to the nearest whole number, y = 10. Substituting y back into the equation for angle HGF, we get (9y + 3)° = (9 × 10 + 3)° = 90° + 3° = 93°. Therefore, the measure of angle HGF is 93 degrees.