Question

If the sum of the measures of the three angles shown is 163

, what is the measure of
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Answer 1

See below.

Explanation:

We are asked to find the measure of ∠CEB.

We already know that the 3 angles combined have a total sum of 163°.

Let's set the 3 angles equal to 163°.

`x-10+4x +2x+5=163`

Now, we should Combine Like Terms.

What is Combining Like Terms?

Combining Like Terms is adding, or subtracting together 2 or more numbers or variables that are alike.

For example, if we were given the expression;

`5x + 3 - 2x + 9`

We should combine 5x and 2x, 3 and 9 since they are like terms.

For our equation;

`x-10+4x +2x+5=163`

We should combine x, 4x, and 2x. We also should combine -10, 5, and 163.

Afterwards, we should have:

`7x=168`

Simplify:

`x= 24`

Substitute 24 within the value of x in the given expression for ∠CEB.

Substitute:

`-10 + 4(24) = 86`

The measure of ∠CEB = 86°