1. The inscribed angle, angle P is congruent to angle S, while angle Q is congruent to angle R.
2. If the measure of angle RQS is 64 degrees, then the measure of arc RS is 128. It is because the inscribed angle is half of its intercepted arc.
3. If the measure of arc PQ is 85, then the measure of angle PRQ is 42.5 degrees.
4. Since angle PQS is congruent to angle SRP, we can equate the two of them and solve for value of x. So:
angle PQS = angle SRP
5x + 3 = 4x + 10
5x - 4x = 10 -3
x = 7
Therefore, the value of x is 7.
To solve for the measure of angle PQS, simply substitute the value of x which is 7. So: PQS = 5x + 3 = 5(7) + 3 = 35 + 3 = 38 degrees
Hence, angle PQS measures 38 degrees.
Since angle SRP is congruent to angle PQS which measures 38 degrees, hence, angle SRP also measures 38 degrees.
The angle SRP intercepts the arc PS. Since angle SRP measures 38 degrees wherein the intercepted arc measures twice the inscribed angle, then, arc PS measures 76.
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INSCRIBED ANGLE AND INTERCEPTED ARC
Answers with Step-by-step explanation:
1. The inscribed angle, angle P is congruent to angle S, while angle Q is congruent to angle R.
2. If the measure of angle RQS is 64 degrees, then the measure of arc RS is 128. It is because the inscribed angle is half of its intercepted arc.
3. If the measure of arc PQ is 85, then the measure of angle PRQ is 42.5 degrees.
4. Since angle PQS is congruent to angle SRP, we can equate the two of them and solve for value of x. So:
angle PQS = angle SRP
Therefore, the value of x is 7.
To solve for the measure of angle PQS, simply substitute the value of x which is 7. So: PQS = 5x + 3 = 5(7) + 3 = 35 + 3 = 38 degrees
Hence, angle PQS measures 38 degrees.
Since angle SRP is congruent to angle PQS which measures 38 degrees, hence, angle SRP also measures 38 degrees.
The angle SRP intercepts the arc PS. Since angle SRP measures 38 degrees wherein the intercepted arc measures twice the inscribed angle, then, arc PS measures 76.
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