Question

LACB is a secant angle of circle F. mAB - 115° and mDE -25°. Find the measure

of ZACB.
C
D
A
25°
F
E
115
B

Answer 1

By applying the theorem of intersecting secants to circle F, the measure of angle ACB is: A. 45°.

In Mathematics and Euclidean Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants to the circle, we can reasonably and logically deduce that the measure of angle ACB or m∠ACB can be calculated as follows:

m∠ACB = 1/2(mAB – mDE)

By substituting the given arc measures, we have the following;

m∠ACB = 1/2(115 – 25)

m∠ACB = 1/2 × 90

m∠ACB = 45°.