Question

∠A and ∠B are vertical angles. If m∠A=(7x−20)⁰ and m∠B=(6x−1)⁰ , then find the measure of ∠A.

A) 7x−20 degrees
B) 6x−1 degrees
C) 13x−21 degrees
D) x−21 degrees

Answer 1

By setting the expressions for vertical angles ∖A and ∖B equal, we solve for 'x' and find that the measure of ∖A is 113°, which corresponds to answer A) 7x−20 degrees.

Step-by-step explanation:

∖A and ∖B are vertical angles, which means they are opposite each other when two lines intersect and are equal in measure. Given that the measure of ∖A is (7x−20)° and the measure of ∖B is (6x−1)°, and knowing that vertical angles have the same measure, we can set the expressions equal to each other to find the value of 'x':

7x − 20 = 6x − 1.

Solving for 'x', we get:

7x − 6x = 20 − 1

x = 19.

Now that we have the value of 'x', we can find the measure of ∖A by substituting 'x' back into the expression for ∖A:

m∖A = 7(19) − 20 = 133 − 20 = 113°.

So the measure of ∖A is 113°, and the correct answer is A) 7x−20 degrees.