Answer:
[tex]\boxed{\bf \angle \: C = 62^{o} }[/tex]
Step-by-step explanation:
The sum of the opposite angle of cyclic quadrilateral is 180°.
First, lets find x...
- [tex]\bf \angle \: B + \angle \: D = {180}^{o} [/tex]
- [tex]\bf (x + 20) + 3x = {180}^{o} [/tex]
- [tex]\bf 4x + 20 = 180[/tex]
- [tex]\bf 4x = 180 - 20[/tex]
- [tex]\boxed{\bf x = {40}^{o}} [/tex]
Now, let's find the measure of angle C....
- [tex]\bf \angle \: a + \angle \: C = {180}^{o} [/tex]
- [tex]\bf 2x + 38 + \angle \: C = {180}^{o} [/tex]
- [tex]\bf 2(40) + 38 + \angle \: C = {180}^{o} [/tex]
- [tex]\bf \angle \: C = 180 - 80 - 38[/tex]
- [tex]\boxed{\bf \angle \: C = {62}^{o}}[/tex]
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