Question

The measure of the angles of a triangle are shown in the figure below. solve for x.

Answer 1

• x° = 12°

Step-by-step explanation:

❁ Hello! ❁

The sum of the measures of the angles of a triangle is 180°.

81° + 57° + (2x + 18)° = 180°

138° + (2x + 18)° = 180°

(2x + 18)° + 138° = 180°

2x + 18° = 180° - 138°

2x + 18° = 42°

2x = 42° - 18°

2x = 24°

x° = 24° ÷ 2

x° = 12°

Success! ☺️

Answer 2

`\boxed {\boxed {\sf x= 12}}`

Explanation:

We are asked to solve for x. We are given a triangle and all 3 angles are labeled. We know that the sum of the angles in a triangle must be 180 degrees. Therefore, the given angles: 81, 57, and (2x+18) must add to 180. We can set up an equation.

`81+57+ (2x+18)= 180`

Now we can solve for x. Begin by combing like terms on the left side of the equation. All the constants (terms without a variable) can be added.

`(81+57+18)+2x=180`

`156+2x=180`

We will solve for x by isolating it. 156 is being added to 2x. The inverse operation of addition is subtraction. Subtract 156 from both sides of the equation.

`156-156+2x=180-156 \\2x=180-156 \\2x= 24`

x is being multiplied by 2. The inverse operation of multiplication is division. Divide both sides by 2.

`2x/2= 24/2 \\x= 24/2 \\x=12`

In this triangle, x is equal to 12.