Answer:
x = 11
Explanation:
Pre-Solving
We are given a circle.
We know that arc DC is equal to 95°, and that arc CE is 10x+3.
We also know that m<DCE = 76°.
We want to find the value of x.
Recall that an entire circle is 360 degrees in measure.
Also recall that an angle that is inside a circle (an inscribed angle) is half the value of the arc it intercepts.
Solving
We can see that <DCE is an inscribed angle; the arc it intercepts is arc DE.
Based on what we know from above, arc DE is twice the value of <DCE.
This means, arc DE = 2(76°) = 152°
As stated above, a circle's full measure is 360 (degrees).
This means that the sum of all the arcs equals 360.
So, arc CD + arc DE + arc CE = 360
Substitute the values we know to get:
95 + 152 + arc CE = 360
247 + arc CE = 360
arc CE = 113
Recall that the value of arc CE is 10x + 3.
So:
10x + 3 = 113
Subtract 3 from both sides.
10x = 110
Divide by 10.
x = 11