By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.
Then using that we will see that the measure of angle BAC is 63 degrees.
How to find the value of x?
On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:
(2x + 3) = (4x - 5)
Solving the linear equation for x we get:
2x + 3 = 4x - 5
3 + 5 = 4x - 2x
8 = 2x
8/2 = x = 4
So we can see that the value of x is 4.
Now we want to find the measure of angle BAC.
We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:
m∠BAC + (4x - 5)° = 90°
Replacing the value of x we get:
m∠BAC + (4*8 - 5)° = 90°
m∠BAC + 27° = 90°
m∠BAC = 90° - 27° = 63°
We conclude that the measure of angle BAC is 63 degrees.
If you want to learn more about vertical angles:
https://brainly.com/question/14362353
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