Exercise 44 Page 767

Consider the given diagram.

We want to find the value of m∠ BAC. We know that if two secants or chords intersect inside the circle, then the measure of an angle formed is half the sum of the arcs intercepted by the angle and its vertical angle. m∠ AED = 1/2(mAD+ mCB) Let's substitute the known values and simplify.

m∠ AED = 1/2(mAD+mCB)

SubstituteII

m∠ AED= 95, mAD= 120

95 = 1/2(120+mCB)

MultEqn

LHS * 2=RHS* 2

190 = 120 + mCB

SubEqn

LHS-120=RHS-120

70 = mCB

RearrangeEqn

Rearrange equation

mCB = 70

Recall that the Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. m∠ BAC = 1/2(mCB) Let's substitute mCB for 70^(∘) and simplify.

m∠ BAC = 1/2(mCB)

Substitute

mCB= 70

m∠ BAC = 1/2(70)

MoveRightFacToNum

a/c* b = a* b/c

m∠ BAC = 1 * 70/2

Multiply

Multiply

m∠ BAC = 70/2

CalcQuot

Calculate quotient

m∠ BAC = 35