Question

Point D is in the interior of angle ABC

The measure of angle ABC = 10x-7

The measure of angle ABD = 6x+5

The measure of angle DBC = 36 degrees

What is the measure of angle ABD?

Answer 1

So first, we need to find the measure of x. Let's do that first.
1. You need to find the expression for angle DBC. We can't just have 36 degrees. We need the actual expression.
So, subtract 6x + 5 from 10x - 7. This will give us the expression we need.
→    (10x - 7) - (6x + 5) = 4x - 12
2. Have 36 and 4x - 12 equal each other. This will help us find the value of x.
→ 36 = 4x - 12    ⇒    x = 12    <Hopefully you know how I got that. If not, I solved it by adding 12 on both sides to isolate the variable to get 48 = 4x. Then, I divided both sides by 4 to get 12.>
3.  Now we know the value of x. Using the expression 6x + 5, substitute 12 for x. 
→ 6 (12) + 5    ⇒    72 + 5 = 77

Therefore, the measure of angle ABD is 77 degrees.

Answer 2

The interior of and angle divides the angle into different segment.

The measure of $\angle ABD$ is $77^o$

Given that:

$\angle ABC = 10x - 7$

$\angle ABD = 6x + 5$

$\angle DBC = 36$

Since D is in the interior of $\angle ABC$, then:

$\angle ABC = \angle ABD + \angle DBC$

So, we have:

$10x - 7 = 6x + 5+ 36$

Collect like terms

$10x - 6x = 7 + 5 + 36$

$4x = 48$

Divide both sides by 4

$x = 12$

Recall that:

$\angle ABD = 6x + 5$

So, we have:

$\angle ABD = 6 \times 12 + 5$

$\angle ABD = 77$

Hence, the measure of $\angle ABD$ is $77^o$

See attachment for illustration of the angles

Read more about interior of angles at:

https://brainly.com/question/2125016