Problem 9.
Using the Angle Addition Postulate,
m<QRS + m<SRT = m<QRT
Now we replace the measures of the three angles above with the value or expressions we are given, and we solve for x.
2x + 8 + 3x + 14 = 82
5x + 22 = 82
5x = 60
x = 12
m<QRS = 2x + 8 = 2(12) + 8 = 24 + 8 = 32
Answer: 32 degrees
Problem 10.
Using the Angle Addition Postulate,
m<ABC + m<CBD = m<ABD
Now we replace the measures of the two angles above with the values we are given, and solve for the unknown angle.
115 + m<CBD = 180
m<CBD = 180 - 115
m<CBD = 65
Answer: m<CBD = 65 degrees
