Question

Quadrilateral BCDE is inscribed in circle A. The measure of ⏜ is 73°. The measure of ⏜ is 53° and the measure of ⏜ is 102°.

Determine the measure of ∠ BCD.

Answer 1

117

Explanation:

Angle BCD intercepted arc is Arc DEB.

We know DE measure but we need to find EB measure.

Since a circle circumference add up to 360, we can add all of the known arcs up to 360 to find the missing arc.

`73 + 53 + 102 + x = 360`

`126 + 102 + x = 360`

`228 + x = 360`

`x = 132`

So arc EB measure 132.

Arc eb and de.

132+102=234.

Angle BCD is inscribed angle of Arc DEB, so that means angle BCD is half of Arc DEB.

`(234)/(2) = 117`