Math  /  Geometry

QuestionFind the measure of angle CC.
The measure of angle CC is \square

Studdy Solution

STEP 1

1. We are given a triangle ABC\triangle ABC.
2. The sum of the angles in any triangle is 180180^\circ.
3. We need to find the measure of angle CC.

STEP 2

1. Set up an equation using the sum of the angles in a triangle.
2. Solve for xx.
3. Find the measure of angle CC.

STEP 3

Write the equation for the sum of the angles in ABC\triangle ABC:
x+(x+20)+(x+40)=180 x + (x + 20) + (x + 40) = 180

STEP 4

Simplify the equation:
x+x+20+x+40=180 x + x + 20 + x + 40 = 180 3x+60=180 3x + 60 = 180

STEP 5

Isolate xx by subtracting 6060 from both sides:
3x=18060 3x = 180 - 60 3x=120 3x = 120

STEP 6

Divide both sides by 33 to solve for xx:
x=1203 x = \frac{120}{3} x=40 x = 40

STEP 7

Substitute x=40x = 40 into the expression for angle CC:
C=x=40 C = x = 40^\circ
The measure of angle CC is:
40 \boxed{40^\circ}

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