Question

geometry module 2 quiz 1 angles. show all work for full credit. for questions 1 and 2 use the image to the right. 1. what type of angle is ∠abc? a acute b right c obtuse d straight. 2. which is true? f m∠ebf = 140 g m∠ebf = 90 h m∠ebf = 50 j m∠ebf = 40. 3. which pair of angles are vertical angles? a ∠rst, ∠tsu b ∠tsu, ∠usv c ∠rsx, ∠tsu d ∠rsx, ∠xsw. for questions 5 - 7 use the image to the right. find the value of y. find m∠1. find the value of x.

Explanation:

Step1: Analyze vertical - angle relationship

Vertical angles are equal. For the angles involving \(y\), assume \((10y + 10)^{\circ}\) is a right - angle (from the hand - written work). So we set up the equation \(10y+10 = 90\).

Step2: Solve the equation for \(y\)

Subtract 10 from both sides of the equation \(10y+10 = 90\):
\[

$$\begin{align*} 10y+10-10&=90 - 10\\ 10y&=80 \end{align*}$$

\]
Then divide both sides by 10: \(y=\frac{80}{10}=8\).

For the angles involving \(x\), assume \(5x + 4x=90\) (from the hand - written work, likely a right - angle split into two adjacent angles).

Step3: Combine like terms

\(5x+4x=(5 + 4)x=9x\). So the equation becomes \(9x = 90\).

Step4: Solve for \(x\)

Divide both sides of the equation \(9x = 90\) by 9: \(x=\frac{90}{9}=10\).

For finding \(m\angle1\), assume vertical - angle relationship. If the vertical angle to \(\angle1\) is related to the other given angles. Let's assume the sum of angles in a triangle or linear - pair relationships. But from the given work, it's not clear about the full context for \(\angle1\). However, if we consider the fact that vertical angles are equal. If we assume the angle \((8y-16)^{\circ}\) is related to \(\angle1\) by vertical - angle property. Substitute \(y = 8\) into \((8y-16)\):
\[

$$\begin{align*} 8y-16&=8\times8-16\\ &=64 - 16\\ &=48 \end{align*}$$

\]

Answer:

\(y = 8\), \(x = 10\), \(m\angle1=48^{\circ}\)