Question

question 13, 2.7.29 part 1 of 2 find the value of each variable and the measure of each angle. (5x - 44)° (4y - x - 12)° (x + 12)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x - 44=x + 12\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(5x-x-44=x - x+12\), which simplifies to \(4x-44 = 12\). Then add 44 to both sides: \(4x-44 + 44=12 + 44\), so \(4x=56\). Divide both sides by 4: \(x=\frac{56}{4}=14\).

Step3: Use another vertical - angle property

The other pair of vertical angles gives \(4y-x - 12=5x - 44\). Substitute \(x = 14\) into this equation: \(4y-14 - 12=5\times14-44\).

Step4: Simplify the right - hand side

First, calculate \(5\times14-44=70 - 44 = 26\). So the equation becomes \(4y-26 = 26\).

Step5: Solve for \(y\)

Add 26 to both sides: \(4y-26 + 26=26 + 26\), so \(4y=52\). Divide both sides by 4: \(y=\frac{52}{4}=13\).

Answer:

\(x = 14\)
\(y = 13\)