Question

In QRS, mQ= 8x-17,mR=19x+4,and mS=5x+1. Classify QRS by its angles and sides

Answer 1

Answer:

Option (3) and Option (5)

Step-by-step explanation:

By the property of a triangle,

Sum of interior angles of a triangle is 180°.

m∠Q + m∠R + m∠S = 180°

By substituting the measures of angles in the equation,

(8x - 17)° + (19x + 4)° + (5x + 1)° = 180°

32x - 12 = 180

32x = 192

x = 6

m∠Q = (8x - 17)° = 48 - 17

                          = 31°

m∠R = (19x + 4)° = 114 + 4

                           = 118°

m∠S = (5x + 1) = 30 + 1

                       = 31°

Since, one interior angle measures 118° which is grater than 90°.

Therefore, triangle QRS is an obtuse triangle.

Since, m∠Q = m∠R = 31°

It's an isosceles triangle.

Option (3) and Option (5) are the correct options.