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vlada-n [284]
3 years ago
8

The measure of the exterior angle of the triangle is ___

Mathematics
2 answers:
mr_godi [17]3 years ago
4 0

Answer: 114°

Step-by-step explanation:

<h2>Concept: </h2>

Here, we need to know the idea of the "Exterior Angle theorem".

<u>The exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.

If you are still confused, then refer to the attachment below for a graphical explanation.

<h2>Solve:</h2>

Given

24 + (2x + 18) = 3x + 6

Put like terms together

24 + 18 + 2x = 3x + 6

Combine like terms

42 + 2x = 3x + 6

Subtract 6 on both sides

42 + 2x - 6 = 3x + 6 - 6

36 + 2x = 3x

Subtract 2x on both sides

36 + 2x - 2x = 3x - 2x

x = 36

Exterior angle = 3x + 6 = 3(36) + 6 = 114°

Hope this helps!! :)

Please let me know if you have any questions

Verizon [17]3 years ago
4 0
<h3>We know sum of two interior angles=exterior angle</h3>

\\ \sf\longmapsto 2x+18+24=3x+6

\\ \sf\longmapsto 2x+42=3x+6

\\ \sf\longmapsto 2x-3x=6-42

\\ \sf\longmapsto -x=-36

\\ \sf\longmapsto x=36

<u>E</u><u>x</u><u>t</u><u>e</u><u>r</u><u>i</u><u>o</u><u>r</u><u> </u><u>a</u><u>n</u><u>g</u><u>l</u><u>e</u>

\\ \sf\longmapsto 3x+6

\\ \sf\longmapsto 3(36)+6

\\ \sf\longmapsto 108+6

\\ \sf\longmapsto 114°

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