Question

In ∠Q, name the bisected angles 1 and 2. If m∠1 is 4x + 3y, can m∠Q be determined in terms of x and y? If so, state m∠Q in terms of x and y and explain your reasoning. If not, explain why not.

A) m∠Q = 2(2x + 3y)
B) m∠Q = 4x + 3y
C) m∠Q = 6x + 6y
D) It cannot be determined without more information.

Answer 1

The measure of angle Q, which is bisected into angles 1 and 2, can be determined as 2(2x + 3y) which is 8x + 6y when both equal bisected angles are added together.

Step-by-step explanation:

When an angle is bisected, it is divided into two equal parts. In the case of ∠Q, this means that the measures of both angles 1 and 2, which the bisector creates, are equal. Given that m∠1 is expressed as 4x + 3y, and knowing that angle 1 and angle 2 are equal due to bisection, we can deduce that m∠2 is also 4x + 3y. To find the measure of m∠Q, we add both m∠1 and m∠2 which leads to m∠Q being 2(4x + 3y) or 8x + 6y. Therefore, the answer is: A) m∠Q = 2(2x + 3y).