ab is parallel to pr and pq is parallel to AC and angle a is 90 degree.find angle p.
To find the measure of angle P, we need to use the properties of parallel lines and angles formed by a transversal.
Given that AB is parallel to PR and PQ is parallel to AC, we can see that angles B and R are corresponding angles and angles Q and C are also corresponding angles.
Since angle A is a right angle (90 degrees), we know that the sum of angle A and angle B is also 90 degrees. This is because angles A and B are adjacent angles forming a right angle.
We can express this relationship as:
Angle A + Angle B = 90 degrees
Since angles B and R are corresponding angles, they are congruent. Therefore, we can replace angle B with angle R:
Angle A + Angle R = 90 degrees
Similarly, since angles Q and C are corresponding angles, they are congruent. Therefore, we can replace angle C with angle Q:
Angle A + Angle R = 90 degrees
Now, since the sum of the angles of a triangle is always 180 degrees, we know that angle P + angle R + angle Q = 180 degrees.
We can substitute angle R with angle A (since angle R and angle A are equal) and angle Q with angle B (since angle Q and angle B are equal):
Angle P + Angle A + Angle B = 180 degrees
Substituting the value of angle A + angle B (which is 90 degrees) into the equation:
Angle P + 90 degrees = 180 degrees
Now, we can isolate angle P by subtracting 90 degrees from both sides of the equation:
Angle P = 180 degrees - 90 degrees
Simplifying the right side:
Angle P = 90 degrees
Therefore, angle P is 90 degrees.