Question

18 multiple choice 2 points the triangle in the picture below represents part of a house. based on the angle measures in the picture, what is the value of x? 72 144 108 54 19 multiple choice 2 points in △abc, m∠a = x, m∠b = 2x + 2, and m∠c = 3x + 4. what is the value of x? 29 59 61 31

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation for the first triangle

For the first triangle with angles \(x\), \(36^{\circ}\), and \(36^{\circ}\), we have the equation \(x + 36+36=180\).

Step3: Solve the equation for the first triangle

\[

$$\begin{align*} x+72&=180\\ x&=180 - 72\\ x&=108 \end{align*}$$

\]

Step4: Set up the equation for the second triangle

For \(\triangle ABC\) with \(m\angle A=x\), \(m\angle B = 2x + 2\), and \(m\angle C=3x + 4\), we use the angle - sum property: \(x+(2x + 2)+(3x + 4)=180\).

Step5: Simplify the equation for the second triangle

\[

$$\begin{align*} x+2x+2 + 3x+4&=180\\ 6x+6&=180 \end{align*}$$

\]

Step6: Solve the equation for the second triangle

\[

$$\begin{align*} 6x&=180 - 6\\ 6x&=174\\ x&=29 \end{align*}$$

\]

Answer:

1. C. 108
2. A. 29