Question

Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C?

Answer 1

Answer:

$\boxed{\bf \angle \: C = 62^{o} }$

Step-by-step explanation:

The sum of the opposite angle of cyclic quadrilateral is 180°.

First, lets find x...

• $\bf \angle \: B + \angle \: D = {180}^{o}$
• $\bf (x + 20) + 3x = {180}^{o}$
• $\bf 4x + 20 = 180$
• $\bf 4x = 180 - 20$
• $\boxed{\bf x = {40}^{o}}$

Now, let's find the measure of angle C....

• $\bf \angle \: a + \angle \: C = {180}^{o}$
• $\bf 2x + 38 + \angle \: C = {180}^{o}$
• $\bf 2(40) + 38 + \angle \: C = {180}^{o}$
• $\bf \angle \: C = 180 - 80 - 38$
• $\boxed{\bf \angle \: C = {62}^{o}}$

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