Question

3. What is the measure of remote angle, LA?
80
B

Answer 1

m<A = 40°

m<C = 113°

Explanation:

Problem 1:

m<A = ½(arc BC) (Inscribed angle theorem)

Substitute

m<A = ½(80°)

m<A = 40°

Problem 2:

Given that m<A = 67°

Recall: angels that are opposite each other in any given inscribed quadrilateral are supplements of each other.

Thus, it implies that:

m<A + m<C = 180°

Substitute

67° + m<C = 180°

Subtract 67° from each side

m<C = 180° - 67°

m<C = 113°