Answer:
x = 6
Explanation:
Pre-Solving
We are given ABCD, which the problem gives as a parallelogram.
We are also given that the measure of ∠B is 12x + 3 and the measure of ∠A is 105°.
Recall that a parallelogram is made up of 2 pairs of parallel sides. This means that CB is parallel to DA and CD is parallel to BA.
- Because we know that BC is parallel to DA, we can consider line BA to be a transversal of those two lines. This makes ∠B and ∠A same-side interior angles, which are equal to 180 degrees.
Solving
Based on the above information, we know that:
m∠B + m∠A = 180°
Substitute what we know into the equation (we can disregard the degree sign).
12x + 3 + 105 = 180
Add the numbers together
12x + 108 = 180
Subtract.
12x = 72
Divide.
x = 6
So, x is equal to 6.