In <pqr if m<p is 14 less than five times x m<q is five less than x and m<r is nine less than twice x find x and the measures of each angle

Question

Find x and the measure of each angle

Answer 1

I'm assuming that PQR is a triangle. Remember that the sum of all three angles must be 180º. Be careful with the wording here and make sure you write each expression in the correct order. Fourteen less than five times x is 5x-14, five less than x is x-5, and nine less than twice x is 2x-9. Put all that together and you get the equation

5x-14 + x-5 + 2x-9 = 180. Combine like terms and you have 8x -28 = 180. Add 28 to both sides of the equation and you get 8x = 208. Divide both sides by 8 and x = 26. Plug that value back into each angle expression to get their values. 5(26)-14 = 116, 26-5 = 21, and 2(26)-9 = 43. To check add the three angles to make sure you have a sum of 180. 116 + 21 + 43 = 180.

Answer 2

Assuming PQR is a triangle whose interior angles sum to 180.

so <P + <Q + <R = 180

substituting given values in x:

5x - 14 + x - 5 + 2x - 9 = 180

8x - 28 = 180

8x = 208

x = 26

substituting x into given values in x:

<P = 5x - 14 = 5(26) - 14 = 116

<Q = x - 5 = 26 - 5 = 21

<R = 2x - 9 = 2(26) - 9 = 43