Question

1. a ray and a line intersect to form $\angle 1$ and $\angle 2$ as shown below. if $m\angle 1 = (3x + 22)$ and $m\angle 2 = (2x + 8)$, what is the measure of $\angle 1$? $\bigcirc$ a. $112^\circ$ $\bigcirc$ b. $58^\circ$ $\bigcirc$ c. $30^\circ$ $\bigcirc$ d. $68^\circ$ 2. a ray and a line intersect to form $\angle 1$ and $\angle 2$ as shown below. if $m\angle 1 = (3x + 22)$ and $m\angle 2 = (2x + 8)$, what is the measure of $\angle 2$? $\bigcirc$ a. $58^\circ$ $\bigcirc$ b. $112^\circ$ $\bigcirc$ c. $30^\circ$ $\bigcirc$ d. $68^\circ$

Explanation:

Problem 1

Step1: Identify angle relationship

∠1 and ∠2 are supplementary (form a linear pair), so \( m\angle1 + m\angle2 = 180^\circ \).
\( (3x + 22) + (2x + 8) = 180 \)

Step2: Solve for x

Combine like terms: \( 5x + 30 = 180 \)
Subtract 30: \( 5x = 150 \)
Divide by 5: \( x = 30 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 30 \) into \( 3x + 22 \):
\( 3(30) + 22 = 90 + 22 = 112^\circ \)

Step1: Use x from Problem 1

From Problem 1, \( x = 30 \).

Step2: Find \( m\angle2 \)

Substitute \( x = 30 \) into \( 2x + 8 \):
\( 2(30) + 8 = 60 + 8 = 68^\circ \)

Answer:

A. \( 112^\circ \)

Problem 2