In isosceles triangle PQR with PQ equals QR, and m angle Q is 92 degrees, the measure of angle P is found to be 44 degrees due to the property that angles opposite to equal sides are equal.
We have a triangle PQR where PQ equals QR, which tells us that it is an isosceles triangle. This means that two sides are equal, and the angles opposite those sides are also equal. Given that the measure of angle Q (m angle Q) is 92 degrees, we can determine the measure of angle P (m angle P) by using the properties of an isosceles triangle.
In every triangle, the sum of the angles equals 180 degrees. If we denote the measure of angle P as x, then angle Q, which we know measures 92 degrees, is equal to the measure of angle R (since it's isosceles and PQ equals QR). Therefore, the equation to find x is:
x + 92 + x = 180
Combining like terms we get:
2x + 92 = 180
Subtracting 92 from both sides gives:
2x = 88
Dividing both sides by 2 to solve for x gives:
x = 44
So, the measure of angle P is 44 degrees.