Question

lines ac and bd intersect at point o. lines ac and bd intersect at point o. if m∠aod = (7x − 5)° and m∠boc = (3x + 15)°, what is m∠boc? a. 5° b. 30° c. 39° d. 60°

Answer 1

B. 30°

Explanation:

Pre-Solving

We are given that lines AC and BD intersect at O, and that m∠AOC = 7x - 5 and m∠BOC = 3x + 15.

If we draw the two lines, we can see that the two angles are vertical angles.

Recall that vertical angles are congruent.

This means m∠AOC = m∠BOC, or 7x - 5 = 3x + 15

Solving

We can evaluate the latter equation.

7x - 5 = 3x + 15

Add 5 to both sides.

7x = 3x + 20

Subtract 3x from both sides.

4x = 20

Divide both sides by 4.

x = 5

Plug 5 as x in 3x + 15 to get m∠BOC.

m∠BOC = 3(5) + 15 = 15 + 15 = 30°.

So, this answer is B.

See image to see a graph of the lines.