Angle ABC and ange DBE are vertical angles,the measure of angle ABC =3x+20, and the measure or angle DBE =4x-10. Write and solve an equation to find the measure of angle ABC and the measure of angle DBEin
To find the measure of angles ABC and DBE, we can set up the equation:
3x + 20 = 4x - 10
Subtract 3x from both sides:
20 = x - 10
Add 10 to both sides:
30 = x
Now we can substitute the value of x back into the original equations to find the measure of angles ABC and DBE:
Angle ABC = 3x + 20 = 3(30) + 20 = 90 + 20 = 110 degrees
Angle DBE = 4x - 10 = 4(30) - 10 = 120 - 10 = 110 degrees
Therefore, the measure of angle ABC is 110 degrees and the measure of angle DBE is 110 degrees.
To solve the problem, we'll set the two angles equal to each other since they are stated as being vertical angles.
So, we have:
3x + 20 = 4x - 10
Now, let's solve for x.
First, we'll isolate the x terms by subtracting 3x from both sides of the equation:
20 = x - 10
Next, we'll isolate the constant term by adding 10 to both sides of the equation:
30 = x
Now that we have found the value of x, we can substitute it back into either of the original equations to find the measure of angle ABC or DBE.
Using the equation 3x + 20 = 4x - 10, let's substitute x = 30 into it:
3(30) + 20 = 4(30) - 10
90 + 20 = 120 - 10
110 = 110
Therefore, the measure of angle ABC is 110 degrees.
Similarly, we can find the measure of angle DBE by substituting x = 30 into the equation 4x - 10:
4(30) - 10 = 120 - 10
120 - 10 = 110
Hence, the measure of angle DBE is also 110 degrees.