Answer:
x = 26 and the angles are P = 116, Q = 21 and R = 43
Step-by-step explanation:
A triangle has three sides and three angles. Thse angles have been givrn in word description and need to be written in algebraic form to enable us calculate:
P = 14 less than five times x = 5x - 14
Q = five less than x = x - 5
R = nine less than twice x = 2x - 9
The sum of all three angles in a triangle must equal 180 degrees, so we have;
5x - 14 + x - 5 + 2x - 9 = 180
5x + x + 2x - 14 - 5 - 9 = 180
8x - 28 = 180
8x = 180 + 28 = 208
x = [tex]\frac{208}{8}[/tex] = 26
Therefore:
P = 5x - 14 = 5(26) - 14 = 130 - 14 = 116
Q = x - 5 = 26 - 5 = 21
R = 2x - 9 = 2(26) - 9 = 52 - 9 = 43
