Question

3 lines are shown. A line with points T, R, W intersects a line with points S, R, W at point R. Another line extends from point R to point U between angle T, R, V. Angle V R W is (3 x) degrees and angle T R S is (2 x + 18) degrees.
What is m∠SRW?

18
54
126
108

Answer 1

Answer:

m∠SRW = $126^{o}$

Step-by-step explanation:

Given: <VRW = 3x

          <TRS = (2x + 18)

What is m∠SRW?

<TRS = <VRW (vertically opposite angles)

2x + 18 = 3x

18 = 3x - 2x

x = 18

<VRW = 3x = 3 x 18 = $54^{o}$

<TRS = (2x + 18) = 92 x 18 + 18)

           = $54^{o}$

Also,

<TRV = <SRW (vertically opposite angles)

So that,

<TRU + <URV = <SRW

But,

<TRV + <SRW + <TRS + <VRW = $360^{o}$

<TRV + <SRW +  $54^{o}$ +  $54^{o}$ = $360^{o}$

<TRV + <SRW + $108^{o}$ = $360^{o}$

<TRV + <SRW = $360^{o}$ -  $108^{o}$

<TRV + <SRW = $252^{o}$

2 <SRW = $252^{o}$    (∵ <TRV = <SRW)

<SRW = $\frac{252}{2}$

           = $126^{o}$

Therefore,

m<SRW = $126^{o}$