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

short answer its 126 so C.

Explanation:

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Answer 2

m∠SRW =
`126^(o)`

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 =
`(252)/(2)`

=
`126^(o)`

Therefore,

m<SRW =
`126^(o)`