Question from-l
- From left to right, horizontal line segment upper P upper V includes the following points:
- Upper P
- Upper Q
- Upper R
- Upper S
- Upper T
- Upper V
- Points upper X and upper U are each below line segment upper P upper V.
- From left to right, the following 2 overlapping triangles are formed between points on line segment upper P upper V and points upper X and upper U:
- Triangle upper Q upper X upper S
- Triangle upper R upper U upper T
- Line segments upper R upper U and upper S upper X intersect at point upper W.
- A note indies the figure is not drawn to scale.
In the figure shown, points , , , and lie on line segment , and line segment intersects line segment at point . The measure of is , the measure of is , the measure of is , and the measure of is . What is the measure, in degrees, of ?
From left to right, horizontal line segment upper P upper V includes the following points: Upper
Hard-difficulty · SAT Math · Lines, Angles, and Triangles — Triangle sum theorem. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
The correct answer is . The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is degrees. It's given that the measure of is and the measure of is . Since points , , and form a triangle, it follows from the triangle angle sum theorem that the measure, in degrees, of is , or . It's also given that the measure of is . Since and are supplementary angles, the sum of their measures is degrees. It follows that the measure, in degrees, of is , or . Since points , , and form a triangle, and is the same angle as , it follows from the triangle angle sum theorem that the measure, in degrees, of is , or . It's given that the measure of is . Since and are supplementary angles, the sum of their measures is degrees. It follows that the measure, in degrees, of is , or . Since points , , and form a triangle, and is the same angle as , it follows from the triangle angle sum theorem that the measure, in degrees, of is , or .
More Lines, Angles, and Triangles practice questions
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