Multiple Choice
What is the common angle of trianglePQT and triangleRSQ?
Triangle P Q R is shown with two segments drawn inside. Segment P T is drawn from P to T on segment R Q. Segment R S is drawn from R to S on segment P Q. Segments P T and R S intersect at point U inside triangle P Q R.
(1 point)
Responses
anglePQT
Image with alt text: angle PQT
angleSPT
Image with alt text: angle SPT
angleSRQ
Image with alt text: angle SRQ
angleSUT
angle SRQ
To determine the common angle of triangle PQT and triangle RSQ, we need to look at the intersection point U inside the triangle.
Based on the given options, the common angle of these triangles is angle SUT.
Therefore, the correct answer is:
angleSUT
To determine the common angle of triangle PQT and triangle RSQ, we need to analyze the given information and provided options.
First, let's locate the segments mentioned in the question: segment PT drawn from P to T on segment RQ, and segment RS drawn from R to S on segment PQ. These segments intersect at point U inside triangle PQR.
Now we will examine each of the options:
1. anglePQT: This angle refers to the angle formed at vertex Q in triangle PQT. However, this angle is not common to both triangles since it is specific to triangle PQT only.
2. angleSPT: This angle refers to the angle formed at vertex P in triangle PST. However, no information is provided about triangle PST in the given question. Therefore, this angle cannot be the common angle of triangle PQT and triangle RSQ.
3. angleSRQ: This angle refers to the angle formed at vertex R in triangle SRQ. It is important to note that this angle is common to both triangles PQT and RSQ. Therefore, angle SRQ is the common angle of triangle PQT and triangle RSQ.
4. angleSUT: This angle is not mentioned in the given question, and there is no given information to determine its existence or significance.
Based on the analysis, the correct answer is angleSRQ, as it is the common angle of triangle PQT and triangle RSQ