In this isosceles trapezoid:
[tex]\begin{gathered} m\angle T=m\angle R \\ m\angle P=m\angle A \end{gathered}[/tex]
Also, the sum of the intern angles of a trapezoid is 360°. That means:
[tex]\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=\frac{384}{16} \\ x=24 \end{gathered}[/tex]
Now we can substitute the value of x and find the measures of each angle:
[tex]\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}[/tex]
Answer:
x = 24
m∠P=70°
m∠A=70°
m∠R=110°
