Question

In triangle QRS, if QR is congruent to RS, angle Q = 8x - 17, angle R = 19x + 4, & angle S = 5x + 1, find x & the measure of each angle.

Answer 1

x=6

`\angle Q=\angle S=31^(\circ)`

`\angle R=118^(\circ)`

Step-by-step explanation:

We are given that in triangle QRS

`\angle Q=8x-17`

`\angle R=19x+4`

`\angle S=5x+1`

`QR\cong RS`

We have to find the value of x and the measure of each angle

We know that congruent sides make congruent angles

Therefore,
`\angle Q=\angle S`

`8x-17=5x+1`

`8x-5x=1+17`

`3x=18`

`x=(18)/(3)=6`

Substitute the value of x

`\angle Q=8(6)-17=31^(\circ)`

`\angle R=19(6)+4=118^(\circ)`

`\angle S=5(6)+1=31^(\circ)`

Answer 2

Angle Q = 31°

Angle R = 118°

Angle S = 31°

Step-by-step explanation:

If QR is congruent to RS, from figure given we have angle Q = angle S.

Angle Q = 8x -17

Angle R = 19x + 4

Angle S = 5x + 1

We have,

8x -17 = 5x + 1

3x = 18

x = 6

So,

Angle Q = 8*6 -17 = 31°

Angle R = 19*6 + 4 = 118°

Angle S = 5*6 + 1 = 31°