Quadrilateral CDEF is inscribed in circle A. If the m∠C = 9x° and m∠E = 7x + 4°, what is the measure of ∠E?Group of answer choices95°99°81°85°
Question
Quadrilateral CDEF is inscribed in circle A. If the m∠C = 9x° and m∠E = 7x + 4°, what is the measure of ∠E?Group of answer choices95°99°81°85°
Solution
In a circle, an inscribed angle is half of its intercepted arc. Therefore, the measures of ∠C and ∠E should add up to 180° because they intercept the entire circle, which is 360°.
So, we can set up the equation:
9x + 7x + 4 = 180
Combine like terms:
16x + 4 = 180
Subtract 4 from both sides:
16x = 176
Divide both sides by 16:
x = 11
Substitute x = 11 into the expression for m∠E:
m∠E = 7x + 4 = 7(11) + 4 = 77 + 4 = 81°
So, the measure of ∠E is 81°.
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