Question

The drawing shown contains the intersection of two lines.

The measure of ∠1 =20x+21 and the measure of ∠2 =30x-29.
a.Write an equation to determine the measures of both angles.
b. Determine the measures of both angles. Show your work. 96 POINTS PLS HELP ASAP

Answer 1

`\Huge \boxed{x=5}`

`\Huge \boxed{121\°}`

Explanation:

∠1 and ∠2 are vertical angles.

∠1 = ∠2

Part A:

Create an equation and solve for x.

20x + 21 = 30x - 29

Add 29 and -20x on both sides.

20x + 21 + 29 - 20x = 30x - 29 + 29 - 20x

Simplify the equation.

50 = 10x

Divide both sides by 10.

`(50)/(10)` =
`(10x)/(10)`

Simplify the equation.

5 = x

Switch sides.

x = 5

Part B:

Let x = 5

20(5) + 21

Distribute.

100 + 21

Add.

= 121

Since both angles are vertical angles, they are equal.

∠1 = 121°

∠2 = 121°