Question

The drawing shown contains the intersection of two lines. The angle formed above the intersection point is labeled as 2 and the angle formed below the intersection point is labeled as 1.

​The measure of ∠1 = 20x + 21 and the measure of ∠2 = 30x − 29.

a. Create an equation to find the measures of both angles.
b. Find the measures of both angles. Show and explain your work.

Please help!!

Answer 1

a) The equation is 20x + 21 = 30x − 29 and the value of x is 5.

b) The measures of both angles is 121°.

Explanation:

The drawing shown contains the intersection of two lines.

• Two intersecting lines form a pair of vertical angles.
• The vertical angles are opposite angles and are equal in measure.
• Here, ∠1 and ∠2 are vertical angles and are equal to each other.

a) To create an equation to find the measures of both angles:

Since both the angles are equal, the equation can be framed as ∠1 = ∠2 .

⇒ 20x + 21 = 30x − 29

Bring x terms alone on one side of the equation,

⇒ 21 + 29 = 30x - 20x

⇒ 50 = 10x

Divide by 10 on both sides of the equation,

⇒ 50 / 10 = x

⇒ x = 5

∴ The value of x is 5.

b) To find the measures of both angles :

The measure of ∠1 = 20x + 21

Substitute x= 5,

⇒ 20(5) + 21

⇒ 100 + 21

⇒ 121

∴ The measure of ∠1 is 121°

The measure of ∠2 = 30x − 29

Substitute x= 5,

⇒ 30(5) - 29

⇒ 150 - 29

⇒ 121

∴ The measure of ∠2 is 121°