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Paladinen [302]
3 years ago
7

The measure of two opposite interior angles of a triangle are and. The exterior angle of the0x−14x+4triangle measures. Solve for

the measure of the3x4+5exterior angle.
Mathematics
1 answer:
11111nata11111 [884]3 years ago
6 0

Answer:

60 degrees

Step-by-step explanation:

Restructured question:

The measure of two opposite interior angles of a triangle are x−14 and x+4. The exterior angle of the triangle measures 3x-45 . Solve for the measure of the exterior angle.

First you must know that the sum of interior angle of a triangle is equal to the exterior angle

Interior angles = x−14 and x+4

Sum of interior angles = x-14 + x + 4

Sum of interior angles = 2x - 10

Exterior angle = 3x - 45

Equating both:

2x - 10 = 3x - 45

Collect like terms;

2x - 3x = -45 + 10

-x = -35

x = 35

Get the exterior angle:

Exterior angle =   3x - 45

Exterior angle = 3(35) - 45

Exterior angle = 105 - 45

Exterior angle = 60

Hence the measure of the exterior angle is 60 degrees

<em>Note that the functions of the interior and exterior angles are assumed. Same calculation can be employed for any function given</em>

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