Question

You are building a gazebo for your mom; you want it to look like the picture below.

a. Using geometry, name which quadrilaterals you see in the picture.
b. What type of quadrilateral is each side of the roof (see inset)?
c. What specific type must it be in order for each side of the roof to fit properly?
d. What is the length of the opposite leg on the side of the roof?
e. What measure is the other base angle?
f. What is the measure of the opposite angles?

Answer 1

a. 1. Trapezoid

2. Rectangle

b. Trapezoid

c. Isosceles trapezoid

d. 6 feet

e. 65°

f. 115°

Explanation:

a. The observed quadrilaterals are;

1. Trapezoid

2. Rectangle

b. Trapezoid

c. Isosceles trapezoid

d. Whereby we have an isosceles trapezoid, the leg lengths are equal. therefore since one of the leg lengths = 6 feet, the other opposite leg on the side of the roof = 6 feet

e. The base angles of an isosceles triangle are equal, therefore, the other base angle is equal to the labelled base angle or 65°

f. The sum of the opposite angles in an isosceles trapezoid = 180°

∴ 65° + Opposite angle = 180°

Opposite angle = 180° - 65° = 115°.