Question

A square has vertices P, Q, R, S labeled clockwise. An equilateral triangle is constructed with vertices P, T, R labeled clockwise. What is the measure of angle P in degrees?

Answer 1

To find the measure of angle P in degrees, we first need to know the measure of angle PRQ (the angle formed between the line segments PR and QR) in degrees. Since we know that angle PRQ is an equilateral triangle, each angle in an equilateral triangle measures 60 degrees. Therefore, angle PRQ measures 60 degrees. Now, we can use the fact that the sum of angles in a quadrilateral is 360 degrees. Since angle PRS is a right angle (90 degrees), we can subtract the measures of angles PRQ, RQS, and PSR from 360 to find the measure of angle P. Therefore, angle P = 360 - angle PRQ - angle RQS - angle PSR = 360 - 60 - 90 - 90 = 120 degrees.

Step-by-step explanation:

To find the measure of angle P in degrees, we first need to know the measure of angle PRQ (the angle formed between the line segments PR and QR) in degrees. Since we know that angle PRQ is an equilateral triangle, each angle in an equilateral triangle measures 60 degrees. Therefore, angle PRQ measures 60 degrees.

Now, we can use the fact that the sum of angles in a quadrilateral is 360 degrees. Since angle PRS is a right angle (90 degrees), we can subtract the measures of angles PRQ, RQS, and PSR from 360 to find the measure of angle P.

Therefore, angle P = 360 - angle PRQ - angle RQS - angle PSR = 360 - 60 - 90 - 90 = 120 degrees.