2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Angle T R V is 95 degrees. mAngleSRW =
The Correct Answer and Explanation is:
To find the measure of ∠SRW given the information:
- Two lines intersect at point R.
- One line has points T, R, W.
- The other line has points S, R, V.
- ∠TRV is 95°.
- We are asked to find m∠SRW.
Step-by-Step Solution
Step 1: Understand the intersection
You have two straight lines:
- Line 1: T — R — W
- Line 2: S — R — V
They intersect at R. So R is the common point, and these lines cross each other.
Since T, R, W lie on one straight line, ∠TRW is a straight angle = 180°.
Similarly, S, R, V lie on a straight line, so ∠SRV = 180°.
Step 2: Use angle relationships
We are given:
- ∠TRV = 95°. This is the angle between ray RT and ray RV.
We are asked to find:
- ∠SRW = the angle between RS and RW.
Let’s look at the diagram logically:
- ∠TRV and ∠SRW are vertical angles. That is, they are opposite each other when two lines intersect.
- Vertical angles are always congruent—they have the same measure.
So,
m∠SRW = m∠TRV = 95°
✅ Final Answer:
m∠SRW = 95°
Explanation
When two straight lines intersect, they form four angles at the point of intersection. Each pair of opposite angles is called vertical angles. A key property of vertical angles is that they are always equal in measure because they are formed by the same two intersecting lines, just in opposite directions.
In this problem, we are told that two lines intersect at point R. One line runs through points T, R, W (forming a straight line), and the other through S, R, V (also a straight line). The angle ∠TRV is given as 95°, which is the angle formed between the directions from R to T and from R to V.
Since these lines intersect, the angle directly opposite ∠TRV—namely ∠SRW—is its vertical angle. The angle ∠SRW is formed between the directions from R to S and R to W.
By the Vertical Angles Theorem, vertical angles are always congruent, meaning they have the same measure. So:
∠TRV = ∠SRW = 95°
This property is fundamental in geometry and helps in many problems involving intersecting lines.
Understanding this concept helps students analyze geometric figures without needing to rely on measurements. Instead, we use relationships and properties like vertical angles, linear pairs, and supplementary angles to determine unknown angle measures logically.
