The drawing shown contains the intersection of two lines.

The figure shows 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

∠2=30x-29

Write an equation to determine the measures of both angles.

Determine the measures of both angles. Show your work.

<1=121°

m<2=121°

Step-by-step explanation:

Recall that vertical angles are formed whenever two straight lines intersect to form an X-shape.

From the diagram, the measure of <1 is 20x+21 and the measure of <2 is 30x-29.

We know that the measure of two vertical angles are congruent.

Therefore we can write the equation:

We group similar terms to get:

Simplify on both sides to get:

Divide both sides by 10 to get:

The measure of angle 1 is 20(5)+21=100+21=121°

Therefore measure of angle 2 is also121°

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

( - 4 , -7 )

all the lines must parallel  

step-by-step explanation:

coordinates of c = ( - 1 , 2 )

3 units left = ( -4 , 2 )

9 units down = ( - 4 , 11 )