Question

In isosceles trapezoid PART, m

Answer 1

In this isosceles trapezoid:

`\begin{gathered} m\angle T=m\angle R \\ m\angle P=m\angle A \end{gathered}`

Also, the sum of the intern angles of a trapezoid is 360°. That means:

`\begin{gathered} 2(5x-10)+2(3x-2)=360 \\ 10x-20+6x-4=360 \\ 10x+6x-20-4=360 \\ 16x-24=360 \\ 16x=360+24 \\ 16x=384 \\ x=(384)/(16) \\ x=24 \end{gathered}`

Now we can substitute the value of x and find the measures of each angle:

`\begin{gathered} m\angle T=m\angle R=5x-10 \\ m\angle T=m\angle R=5\cdot24-10 \\ m\angle T=m\angle R=110\degree \\ \\ m\angle P=m\angle A=3x-2 \\ m\angle P=m\angle A=3\cdot24-2 \\ m\angle P=m\angle A=70\degree \end{gathered}`

Answer:

x = 24

m∠P=70°

m∠A=70°

m∠R=110°