Question

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

Answer 1

`\boxed{\bf \angle \: C = 62^(o) }`

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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