Question

Pls help i need it rn asapppp

Answer 1

(10x + 2)° = 132°

(3x + 9)° = 48°

Explanation:

Consecutive interior angles are a pair of angles formed when a transversal intersects two parallel lines. They are located on the same side of the transversal and inside the parallel lines.

Consecutive interior angles are supplementary, meaning their sum is 180°.

So,

(10x + 2)° + ( 3x + 9)° = 180°

Simplify like terms:

13x + 11 = 180

Subtract 11 on both sides:

13x + 11 - 11 = 180 - 11

13x = 169

Divide both sides by 13.

`\sf (13x)/(13)=(169)/(13)`

x = 13

Now, we can find consecutive interior angles by substituting value of x, we get

(10x + 2)° = (10×13 + 2)° = (130 + 2)° = 132°

(3x + 9)° = (3 × 13 + 9)° = (39 + 9) = 48°

Therefore,

• (10x + 2)° = 132°
• (3x + 9)° = 48°

Answer 2

x = 13

Explanation:

assuming you require to find x and the measure of the angles.

(3x + 9)° and (10x + 2)° are same- side interior angles and sum to 180°

sum the 2 angles and equate to 180, solving for x

3x + 9 + 10x + 2 = 180 ( simplify left side )

13x + 11 = 180 ( subtract 11 from both sides )

13x + 11 - 11 = 180 - 11 ( simplify both sides )

13x = 169 ( divide both sides by 13 )

`(13)/(13)` x =
`(169)/(13)` , that is

x = 13

then by substitution

3x + 9 = 3(13) + 9 = 39 + 9 = 48°

10x + 2 = 10(13) + 2 = 130 + 2 = 132°