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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.

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. class=

Answer :

Answer:

117

Step-by-step 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.

[tex]73 + 53 + 102 + x = 360[/tex]

[tex]126 + 102 + x = 360[/tex]

[tex]228 + x = 360[/tex]

[tex]x = 132[/tex]

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.

[tex] \frac{234}{2} = 117[/tex]

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