Answer:
m∠QPR = 80°
Step-by-step explanation:
Look at the picture.
We know: the sum of the measures of the angles of the triangle is equal to 180 °.
Therefore
In ΔTQR we have the equation:
[tex]\alpha+\beta+130^o=180^o[/tex] subtract 130° from both sides
[tex]\alpha+\beta=50^o[/tex]
In ΔPQR we have the equation:
[tex]2\alpha+2\beta+m\angle QPR=180^o[/tex]
[tex]2(\alpha+\beta)+m\angle QPR=180^o[/tex]
Substitute from the first equation
[tex]\alpha+\beta=50^o[/tex]
[tex]2(50^o)+m\angle QPR=180^o[/tex]
[tex]100^o+m\angle QPR=180^o[/tex] subtract 100° from both sides
[tex]m\angle QPR=80^o[/tex]
