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The measures of the angles of a triangle are shown in the figure below. Solve for x.

The measures of the angles of a triangle are shown in the figure below. Solve for-example-1
User Davykiash
by
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1 Answer

1 vote

Answer:

x = 6

Explanation:

The Triangle Sum Theorem says that the sum of the interior angles in a triangle is always 180°.

Thus, we can find x by making the sum of all the angles in the triangle 180.

(Note before we start the problem that the angle in the the bottom left corner is a right angle and thus its measure is 90°)

90 + 4x + 3 + 63 = 180

(90 + 3 + 63) + 4x = 180

(156 + 4x = 180) - 156

(4x = 24) / 4

x = 6

Thus, x = 6

Optional: Check the validity of the answer:

We can check that our answer is correct by plugging in 6 for x in 4x + 3 and seeing if we get 180 when we add up all the angles in the triangle:

4(6) + 3

24 + 3

27

Thus, the measure of the angle at the top of the triangle is 27. Now let's check that the sum of the three angles equals 180:

90 + 27 + 63 = 180

180 = 180

Thus, our answer is correct.

User Lazarus Thurston
by
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