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 the measure of ∠2=30x−29.
A. Write an equation to determine the measures of both angles.
B.Determine the measures of both angles
Please help asap!!!
"vertical" angles are equal
20 x + 21 = 30 x - 29 ... 50 = 10 x
what does that mean?
the dots
Sure, let's solve this problem step by step.
A. To write an equation to determine the measures of both angles, we need to set up an equation that equates the two angles.
Since the measure of angle 1 is given as 20x + 21 and the measure of angle 2 is given as 30x - 29, we can write the equation:
20x + 21 = 30x - 29
This equation represents the condition where the measures of the two angles are equal.
B. Now, let's solve the equation to determine the measures of both angles.
To solve this equation, we need to isolate x on one side of the equation.
Let's begin by bringing the x terms to one side and the constant terms to the other side:
20x - 30x = -29 - 21
Simplifying the equation, we get:
-10x = -50
Next, we divide both sides of the equation by -10 to solve for x:
x = -50 / -10
Simplifying further, we get:
x = 5
Now that we have the value of x, we can substitute it back into the original expressions for angle 1 and angle 2 to find their measures.
For angle 1:
∠1 = 20x + 21 = 20(5) + 21 = 100 + 21 = 121
Therefore, the measure of angle 1 is 121 degrees.
For angle 2:
∠2 = 30x - 29 = 30(5) - 29 = 150 - 29 = 121
Therefore, the measure of angle 2 is also 121 degrees.
Hence, the measures of both angles are 121 degrees.
I hope this helps!