When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠SRW is 126°.
What is an angle?
When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
What are vertical angles?
Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.
The two of the angles ∠SRT and ∠VRW will be vertically opposite angles, therefore, we can write,
∠SRT = ∠VRW
2x + 18 = 3x
x = 18
Now, the measure of the angle,
∠SRT = 2x + 18 = 54°
∠VRW = 3(18) = 54°
As per the given figure, the sum of ∠TUV will be equal to ∠SRW, because both the angles are vertically opposite angles. Now, since the sum of all the angles about a point is 360°. Therefore, the sum of all the angles about the point R will be,
∠SRW + ∠TRW + ∠VRW + ∠SRW = 360°
54° + ∠SRW + 54° + ∠SRW = 360°
∠SRW = 126°
Hence, the measure of ∠SRW is 126°.
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