Question

∠ABD and ∠CBD form a linear pair. If m∠ABD = 6x - 12 and m∠CBD = x + 31, find the m∠ABD.

A) 31 degrees
B) 7 degrees
C) 13 degrees
D) 19 degrees

Answer 1

To find the measure of angle ABD, we need to understand that angle ABD and angle CBD form a linear pair. By setting up an equation, we can solve for x and then find the measure of angle ABD.

Step-by-step explanation:

To find the measure of angle ABD, we need to understand that angle ABD and angle CBD form a linear pair. A linear pair is a pair of adjacent angles that add up to 180 degrees. In this case, m∠ABD + m∠CBD = 180 degrees.

Substituting the given measures, we have (6x - 12) + (x + 31) = 180. Simplifying the equation, we get 7x + 19 = 180. Solving for x, we find that x = 21.

Now we can find the measure of angle ABD by substituting x back into the expression. m∠ABD = 6(21) - 12 = 114 - 12 = 102 degrees.