Given: m∠3 = 56° Find the following in degrees. (a) mRT (b) mRST

Question

In the figure, R and T are points of tangency.

Given:    m∠3 = 56°

Find the following in degrees.

(a) mRT

  

(b) mRST

Answer 1

Consider the quadrilateral 3TOR, where O is the center. As the sum of the angles in a convex quadrilateral is 360°, m∠3 is 56º, m∠3TO = 90º, and m∠3RO = 90º, m∠TOR = 360° - 56º - 90º - 90º = 124º

m arc RT = m∠TOR = 124º

m arc RST = 360º - 124º = 236°