Question

In triangle ABC, m∠A=(2x+2)∘, m∠C=54∘, and the exterior angle at B is (4x)∘.

Triangle A B C. Angle A is 2 X plus 2 degrees, angle C is 54 degrees, & the exterior angle at B is 4 X degrees.



What is the measure of angle A?
58∘
112∘
28∘
68∘

Answer 1

58°

Explanation:

The exterior angle of a triangle is equal to the sum of the two remote interior angles.

m∠A + m∠C = measure of exterior angle at B

2x + 2 + 54 = 4x

2x + 56 = 4x

2x = 56

x = 28

m∠A = 2x + 2 = 2(28) + 2 = 56 + 2 = 58°

Answer 2

A

Explanation:

Remark

<A + <C = the exterior angle.

Two remote interior angles = the exterior angle that neither connects to.

Remote means that the angles do not share any line in common with the remote angle. One of them might share a line extended with the exterior angle.

Equation

<A + <C = Remote angle connected to the supplement of B

Givens

m<A = 2x + 2

m<C = 54

Remote angle = 4x

Solution

2x + 2 + 54 = 4x Combine like terms on the left

2x + 56 = 4x Subtract 2x from both sides

56 = 4x - 2x

2x = 56 Divide by 2

x = 56/2

x = 28

Answer

<A = 2x + 2

<A = 2*28 + 2

<A = 56 + 2

<A = 58