Given: In ⊙Q, PR contains Q, MR is a tangent, mMP = 116°, mMN = 60° and mMT = 46°.Find the following in degrees.

Question

Consider the following figure.

A circle has center point Q. There are six points, three line segments, and two angles.

1. Five points lie on the circle:
2. M is on the top right; 
3. N is on the top left; 
4. P is on the left, just below center; 
5. V is on the right, just above center; and 
6. T is on the upper right, between M and V.
7. Point R lies outside the circle, on the right.
8. Segment P R passes through center Q and intersects the circle at V.
9. Segment N R intersects the circle at T.
10. Segment M R is tangent to the circle at M.
11. ∠M R N is labeled 1, and ∠P R N is labeled 2.

	Given:     In ⊙Q, PR contains Q, MR is a tangent, mMP = 116°, mMN = 60° and mMT = 46°.
	.

Find the following in degrees.

(a) m∠MRP

 °

(b) m∠1

 °

(c) m∠2

Answer 1

drawing a triangle QRM, ANGLE Q is 64 degrees from the given information and ANGLE M is 90 degrees, so ANGLE R IS 26 degrees, ANGLE R is same as ANGLE MRP.

For ANGLE 2, draw triangle TQN, it isosceles, from given information ANGLE N calculates to 37 degrees. draw triangle RQN. ANGLE QNR is same as ANGLE N = 37degrees. ANGLE RQN is from the given information 124 degrees, so ANGLE 2 = ANGLE NRQ = 19 degrees.

ANGLE 1 = 26-19= 7 degrees.

Answer 2

r=(mp-nv)/2 (arcs)