Question

Lesson 5.4

1 .Find the measurement of the angle indicated for each trapezoid.
2.Find the measure.
3.Solve for [x]. Each figure is a trapezoid.
4.Find the measurement of the angle indicated for each trapezoid.

Answer 1

Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

`m\angle C+130^(\circ)=180^(\circ) \\ \\ m\angle C=50^(\circ)</p><p>`

Question 2

Drawing PR, we form congruent triangles PQR and PSR. Thus, using the sum of angles in a triangle,

`55^(\circ)+24^(\circ)+m\angle Q=180^(\circ) \\ \\ m\angle Q=101^(\circ)`

Question 3

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

`13x+6+70=180 \\ \\ 13x+76=180 \\ \\ 13x=104 \\ \\ x=8`

Question 4

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

`11x+15+19x+15=180 \\ \\ 30x+30=180 \\ \\ 30x=150 \\ \\ x=5 \\ \\ m\angle B=11(5)+15=70^(\circ)`