Question

Can you please help me with this, due tomorrow!!!

Answer 1

Answer is ∠ ACB = 120 degrees

Step by step

Using Exterior Angle Theorem Formula, we know The sum of the exterior angle (ACD) = the sum of two non-adjacent interior opposite angles (CAB) and (ABC)

So we know the equation is

5x -10 = (2x + 2) + (2x + 2)
Combine

5x - 10 = 4x + 4
Subtract 4x from both sides to isolate variable

5x - 4x -10 = 4x - 4x + 4
Combine

x -10 = 4

Add 10 to both sides to solve x

x -10 +10 = 4 + 10
Combine

x = 14

Now we can solve for ∠ ACB

Using the two known angle expressions, substitute in your x value and solve

2x + 2 = CAB
(2)(14) + 2 = CAB
30 = ∠ CAB

2x + 2 = ABC
(2)(14) + 2 = ABC
30 = ∠ ABC

we know the sum of the angles of the triangle = 180 degrees

We know we have angles = 30 and 30

Subtract from 180 to solve for unknown angle

180 - 30 - 30 = 120

This means angle ∠ ACB = 120

We can double check our work because the exterior angle and ∠ ACB are a straight angle, their angles should also equal 180 degrees.

5x - 10 + 120 = 180

5(14) -10 + 120 = 180

70 - 10 + 120 = 180

180 = 180

Problem solved!

Answer 2

120 degrees

Explanation:

Using the exterior angle theorem, we can say 2x+2+2x +2 is equal to 5x-10

2x+2+2x+2= 5x-10

4x+4=5x-10

14=x

Once we found x, we can plug x into the expressions and find the remaining angle using 3 angles = 180 degrees.

2(14) + 2 = 28 + 2 = 30

30 + 30 = 60

180 - 60 = 120

Therefore, the measure of angle ACB is equal to 120 degrees