Exercise 6 Page 745

Consider the given diagram.

We want to find the value of x. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Notice that the inscribed angle C — which measures 3x^(∘) — intercepts AD . Therefore, we can say that mAD is equal to 2(m∠ C). mAD = 2 (m∠ C) ⇒ mAD =2 (3x) The inscribed angle B — which measures (x+24)^(∘) — also intercepts AD. Therefore, mAD is also equal to 2(m∠ B). mAD = 2 (m∠ B) ⇒ mAD = 2 (x+24) Let's equate both expressions and solve for x.

2 (3x) = 2 (x+24)

Multiply

Multiply

6x = 2x + 48

SubEqn

LHS-2x=RHS-2x

4x = 48

DivEqn

.LHS /4.=.RHS /4.

x = 12

Finally, we can evaluate m∠ B.

m∠ B = x + 24

Substitute

x= 12

m∠ B = 12 + 24

AddTerms

Add terms

m∠ B = 36^(∘)