What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77 degrees?

Find the measure of each angle (x + 1) (4x - 56)

To find the measure of angle DBC, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

Given that the measure of angle ABC is 77 degrees, we can write the equation:

4x + 3x + 77 = 180

Combining like terms, we get:

7x + 77 = 180

Subtracting 77 from both sides, we have:

7x = 180 - 77

Simplifying the right side, we get:

7x = 103

Now, divide both sides by 7 to solve for x:

x = 103 / 7

Now, substitute the value of x back into the expression for the measure of angle DBC:

3x = 3 * (103 / 7)

Simplifying, we have:

3x = 309 / 7

Therefore, the measure of angle DBC is 309/7 degrees.

To find the measure of angle DBC, we first need to consider the relationship between the angles in triangle ABC. In a triangle, the sum of all interior angles is always 180 degrees.

So we can set up an equation using the given information:

Angle ABD + Angle DBC + Angle ABC = 180 degrees

Since angle ABD is represented by 4x, angle DBC is represented by 3x, and angle ABC is 77 degrees, we can write:

4x + 3x + 77 = 180

To solve this equation for x, we combine like terms:

7x + 77 = 180

Subtract 77 from both sides of the equation:

7x = 180 - 77
7x = 103

Divide both sides of the equation by 7 to isolate x:

x = 103 / 7
x ≈ 14.71

Now that we have found the value of x, we can substitute it back into the expression for angle DBC:

Angle DBC = 3x
Angle DBC = 3 * 14.71
Angle DBC ≈ 44.13 degrees

Therefore, the measure of angle DBC is approximately 44.13 degrees.