Answer :
Final Answer:
In triangle pqr. ps is the median . The measure of angle prq is 30° and the angle psq has measure of 45°.Then the measure of the angle QPS is 60°.
Explanation:
In triangle PQR, with PS as the median, angle PRQ measuring 30°, and angle PSQ measuring 45°, we can determine the measure of angle QPS using properties of medians and triangle angles.
Step 1: Since PS is the median, it divides QR into two equal segments. This makes angles PSQ and PSR congruent due to the base angles of an isosceles triangle.
Step 2: The sum of angles in a triangle is 180°. Therefore, we can find angle QPS by subtracting angles PRQ and PSR from 180°:
Angle QPS = 180° - angle PRQ - angle PSR.
Step 3: After substituting the given angle measures, we get an initial value for angle QPS as 105°. However, this includes both angle QPS and angle SPQ.
Step 4: To find the measure of angle QPS alone, we need to subtract the known measure of angle SPQ (45°) from the calculated 105°:
Angle QPS = 105° - 45° = 60°.
This means that the measure of angle QPS in triangle PQR is 60°.
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The measure of the angle QPS in triangle PQR is 105 degrees.
In triangle PQR, with angle PRQ as 30° and angle PSQ as 45°, the measure of angle QPS is 105°. This follows from the fact that the angles in a triangle sum up to 180°.
In a triangle, the angles add up to 180 degrees. Given that PRQ is 30 degrees and PSQ is 45 degrees, we can find the measure of angle QPS.
Angle PRQ + Angle PSQ + Angle QPS = 180 degrees
Substitute the given values:
30 + 45 + Angle QPS = 180
Solve for Angle QPS:
Angle QPS = 180 - 30 - 45
Angle QPS = 105 degrees
Therefore, the measure of angle QPS in triangle PQR is 105 degrees.
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