Angle Pairs Unit Test

Question

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Question
Use the image to answer the question.

An illustration shows three rays passing through three points from a common origin point at upper S. Point upper T is to the horizontal left of upper S. A ray from upper S joins upper T with an arrow near upper T. Point upper V is on the top inclined to the right of point upper S. A ray from upper S joins upper V with an arrow near upper V. Point upper R is to top right of point upper S, below point upper V. A ray from upper S joins upper R with an arrow near upper R. Angle upper T upper S upper R is labeled as 157 degrees. Angle upper V upper S upper R as 54 degrees.

What is the measure of ∠TSV

Answer 1

To find the measure of angle \( \angle TSV \), we can use the fact that the angles around point \( S \) sum up to \( 360^\circ \).

Given:

• \( \angle TSR = 157^\circ \)
• \( \angle VSR = 54^\circ \)

First, calculate the sum of the angles at point \( S \):

\[ \angle TSR + \angle VSR + \angle TSV = 360^\circ \]

Plug in the known values:

\[ 157^\circ + 54^\circ + \angle TSV = 360^\circ \]

Now, simplify the left side:

\[ 211^\circ + \angle TSV = 360^\circ \]

Now, solve for \( \angle TSV \):

\[ \angle TSV = 360^\circ - 211^\circ = 149^\circ \]

Therefore, the measure of \( \angle TSV \) is \( 149^\circ \).