Exercise 10 Page 764

Consider the given diagram.

We want to find m∠ JMK. 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∠ KML = 1/2(mHJ+ mLK) Let's substitute the known values and simplify.

m∠ KML = 1/2(mHJ+mLK)

SubstituteII

mHJ= 79, mLK= 77

m∠ KML = 1/2(79+77)

AddTerms

Add terms

m∠ KML = 1/2(156)

MoveRightFacToNum

a/c* b = a* b/c

m∠ KML = 156/2

CalcQuot

Calculate quotient

m∠ KML = 78

Note that ∠ JML is a straight angle, which measures 180^(∘). By the Segment Addition Postulate, we can write the following equation. m ∠ JMK + m ∠ KML = 180 ↓ m∠ JMK + 78 = 180 Finally, let's solve it for m∠ JMK.

m∠ JMK + 78 = 180

SubEqn

LHS-78=RHS-78

m∠ JMK = 102