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Answer :
Final answer:
In a triangle, the sum of the measures of the angles is always 180 degrees. Given that ∠QPS is a right angle of 90 degrees and the measure of ∠QPR is 71 degrees, the measure of ∠RPS is found to be 19 degrees by subtracting the given measures from 180 degrees.
Explanation:
To solve this problem, we need to compensate for the fact that the sum of the measures of the angles in a triangle is 180 degrees. Given that ∠QPS is a right angle, it measures 90 degrees. If the measure of ∠QPR is 71 degrees, we can calculate the measure of ∠RPS by subtracting the measures of ∠QPR and ∠QPS from 180 degrees.
So, we subtract 90 degrees and 71 degrees from 180 degrees which gives us m∠RPS = 180 - 90 - 71 = 19 degrees.
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