Question

angle rqt is a straight angle. what are the measures of angles rqs and tqsmeasures of angles RQSmeasures of angles TQS

Answer 1

From the picture,

∠RQS + ∠TQS = ∠RQT

Replacing with data,

(14x + 2) + (11x + 3) = 180

(14x + 11x) + (2 + 3) = 180

25x + 5 = 180

25x = 180 - 5

25x = 175

x = 175/25

x = 7

Then, the measures of the angles are:

∠RQS = 14x + 2

∠RQS = 14(7) + 2

∠RQS = 98 + 2

∠RQS = 100°

∠TQS = 11x + 3

∠TQS = 11(7) + 3

∠TQS = 77 + 3

∠TQS = 80°