Question

If the measure of angle DBC = (12x - 3), the measure of angle DBE = (5x + 12), and the measure of angle EBC = (3x + 13), find the measure of angle EBC.

Answer 1

To find the measure of angle EBC, we can use the fact that the angles in a triangle add up to 180 degrees. By setting up an equation and solving for x, we can find the value of x and then substitute it back into the equation to find the measure of angle EBC. The measure of angle EBC is 37.7 degrees.

Step-by-step explanation:

To find the measure of angle EBC, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, we have:

angle DBC + angle DBE + angle EBC = 180

Substituting the given measures:

(12x - 3) + (5x + 12) + (3x + 13) = 180

Combine like terms:

20x + 22 = 180

Subtract 22 from both sides:

20x = 158

Divide by 20:

x = 7.9

Now we can substitute this value back into the equation to find the measure of angle EBC:

angle EBC = 3(7.9) + 13 = 24.7 + 13 = 37.7 degrees

Answer 2

Consider the below figure attached with the question.

Given:

m∠DBC = (12x - 3), m∠DBE = (5x + 12), m∠EBC = (3x + 13).

To find:

The measure of ∠EBC.

Solution:

From the figure, it is clear that,

`m\angle DBC-m\angle DBE=m\angle EBC`

Putting the given values, we get

`(12x-3)-(5x+12)=(3x+13)`

`12x-3-5x-12=3x+13`

`7x-15=3x+13`

`7x-3x=15+13`

`4x=28`

Divide both sides by 4.

`x=7`

Now,

`m\angle EBC=(3x+13)^\circ`

`m\angle EBC=(3(7)+13)^\circ`

`m\angle EBC=(21+13)^\circ`

`m\angle EBC=34^\circ`

Therefore, the measure of angle EBC is 34 degrees.