Question

The measures of the three angles of a triangle are given by 18x - 7, 12x + 9 and 4x. What is the measure of the largest angle?

Answer 1

Answer: 87°

Step-by-step explanation:

Sum ange of a supplementary triangle is 180°

Therefore, to get the measure of the largest angle, we add the angles together and equate to 180 to get the value of x first.

18x - 7 + 12x + 9 + 4x = 180°

             34x  + 2        = 180°

              34x              = 180 - 2

              34x              = 178

  Divide through by 34

                              x  = ¹⁷⁸/₃₄

                              x = 5.24.

Now substitute for x to get the measure of the largest angle.

i.               18(5.24) - 7 =  87.32,° to the nearest degree = 87°

ii.              12(5.24) + 9 = 71.88°, to the nearest degree = 72°

iii.              4(5.24)       = 20.96, to the nearest degree = 21°

The largest angle is 87°

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