raise pq and qr are perpendicular point s lies in the interior of angle pqr if measure of the angle pqs equals 4=7a and the measure of angle sqr = 9+4a find the measure of angle pqs and sqr
To find the measures of angles PQS and SQR, we need to use the given information.
First, let's start by defining the angles:
- Angle PQS is the angle formed by the lines PQ and QS.
- Angle SQR is the angle formed by the lines SQ and QR.
We are given that angle PQS measures 4 + 7a, and angle SQR measures 9 + 4a.
Since we know that PQ and QR are perpendicular, we can use the fact that perpendicular lines form right angles.
This means that angle PQS and angle SQR are complementary angles (they add up to 90 degrees).
Therefore, we can set up the equation:
(4 + 7a) + (9 + 4a) = 90
Solving this equation will give us the value of 'a'. Once we find the value of 'a', we can substitute it back to find the measures of angles PQS and SQR.