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

since vertical angles are equal,

3x+20 = 4x-10
x = 30

check:
ABC = 110
DBE = 110

UV=3c+29,VW=-2-4,UW=-4c

Bd Bisect ABC=(6×-10)° and m dbc = (2×+20)°

To solve this problem, we need to use the fact that vertical angles are congruent. Since angle ABC and angle DBE are vertical angles, their measures are equal.

Let's set up an equation by equating the measures of angle ABC and angle DBE:

3x + 20 = 4x - 10

Now, we can solve for x by isolating the variable. Let's start by getting all the terms with x on one side:

3x - 4x = -10 - 20
-x = -30

Next, we can solve for x by dividing both sides of the equation by -1:

x = 30

Now that we have the value of x, we can find the measure of angle ABC and angle DBE by substituting x back into their respective expressions:

Measure of angle ABC = 3x + 20
Measure of angle ABC = 3(30) + 20
Measure of angle ABC = 90 + 20
Measure of angle ABC = 110

Measure of angle DBE = 4x - 10
Measure of angle DBE = 4(30) - 10
Measure of angle DBE = 120 - 10
Measure of angle DBE = 110

Therefore, the measure of angle ABC is 110 degrees, and the measure of angle DBE is also 110 degrees.