Exercise 24 Page 765

Let's begin by drawing a diagram that illustrates the given situation.

We are given that x=260^(∘), which implies that m ADB is 260^(∘). Since CA and CB are tangent to the circle and they intersect each other outside it, we have that y is equal to one half the measure of the difference of the intercepted arcs. y = 1/2(m ADB - m AB) By using the measure of the major arc we will find the measure of the minor arc. m ADB^(260^(∘)) + m AB = 360^(∘) ⇓ m AB = 100^(∘) Finally, let's substitute the measures of both arcs to find the measure of the required angle.

y = 1/2(m ADB - m AB)

SubstituteII

m ADB= 260^(∘), m AB= 100^(∘)

y = 1/2( 260^(∘) - 100^(∘))

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Simplify

SubTerms

Subtract terms

y = 1/2(160^(∘))

Multiply

Multiply

y = 160^(∘)/2

CalcQuot

Calculate quotient

y=80^(∘)