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Solve for x. Please help.

Solve for x. Please help.-example-1
User Kianna
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1 Answer

5 votes

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

User Abincepto
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