Step-by-step explanation:
Let me begin by saying I cannot clearly see the letter assigned to the vertex of the right angle, I will assume it is S.
Some basics that we will use. The sum of all three angles of a triangle is 180 degrees.
The angle of a straight line is 180.
If we begin with the lower left triangle AQS, we are given two angles of the triangle, 25 and 130. The angles of all three angles of a triangle is 180 - 25 - 130 = 25 is the measure of angle ASQ.
Looking at angle PAS we can evaluate the line QP with known angle at QAS of 130. The angle of a straight line is 180, subtract the known angle to get 180 = 130 = 50 is the measure of angle PAS.
We are given that angle PSR is a right angle, and just as in the last angle as part of a line, the angle opposite is 180 - 90 = 90 is the measure of angle PSQ. We determined above that angle ASQ has a measure of 25 degrees, so the measure of the other side is 90 = 25 = 65 8s the measure of angle PSA.
We determined above that angle PAS is 50, and angle PSA is 65, so angle APS is 180 - 50 - 65 = 65 is the measure of angle APS.
The measure of the opposite side of angle APS, angle SPR are equal; 65. Angle SPR is 65, angle PSR is 90 so angle PRS is 180 - 65 - 90 = 25.
NOTICE that triangle PQR, the greater triangle, and the triangle QAS have equal measures of ANGLES, though their side lengths are different.
Iscosoles triangles have at least 2 sides of equal length.
I believe the greater triangle and the two on the left would qualify.
