Question

Given \qquad m \angle ABDm∠ABDm, angle, A, B, D is a straight angle. \qquad m \angle CBD = 8x + 16^\circm∠CBD=8x+16 ∘ m, angle, C, B, D, equals, 8, x, plus, 16, degrees \qquad m \angle ABC = 6x - 60^\circm∠ABC=6x−60 ∘ m, angle, A, B, C, equals, 6, x, minus, 60, degrees Find m\angle ABCm∠ABCm, angle, A, B, C:

Answer 1

To find the measure of angle ABC, we set up an equation with the given expressions for angles CBD and ABC, and knowing that a straight angle is 180 degrees. After solving for x, we substituted it back into the expression for m∠ABC to get the final measure of 36 degrees.

Step-by-step explanation:

The student is asking to find the measure of angle ABC in a situation where angle ABD is a straight angle, and we are given the expressions for angles CBD and ABC in terms of a variable x. A straight angle is equal to 180 degrees, so we can set up an equation based on the fact that the sum of angles CBD and ABC must equal 180 degrees since they form a straight line together with angle ABD.

By setting up the equation:
(8x + 16) + (6x - 60) = 180,
we can solve for x which will then be used to calculate the measure of angle ABC by substituting x back into its expression.

Combining like terms, we get:
14x - 44 = 180
Adding 44 to both sides gives us:
14x = 224
Dividing by 14 gives us:
x = 16

Now we can find m∠ABC by substituting x back into its expression, which results in:
m∠ABC = 6(16) - 60 = 96 - 60 = 36 degrees.