The measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.
Sum of interior angle of a triangle
The sum of interior angle of a triangle is 180 degrees. Applying the theorem to each question.
3) 40 + x + 75 = 180
115 + x = 180
x = 180 - 115
x = 65 degrees
4) p + 40 + 120 = 180
p + 160 = 180
p = 20degrees
5). The triangle is isosceles showing that the base angles are equal.
100 + q + r = 180
100 + 2q = 180
2q = 80
q =r = 40 degrees
Hence the measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.
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