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The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs.
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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= 95, mAD= 120
LHS * 2=RHS* 2
LHS-120=RHS-120
Rearrange equation
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.
mCB= 70
a/c* b = a* b/c
Multiply
Calculate quotient