Question

1. the measure of $angle 2$ is twelve less than five times the measure of $angle 1$. if $angle 1$ and $angle 2$ form a linear pair, find $mangle 2$.

$mangle 2 = square$

Explanation:

Step1: Define variables for angles

Let $m\angle 1 = x$, $m\angle 2 = 5x - 12$

Step2: Use linear pair sum property

Linear pairs sum to $180^\circ$, so:
$$x + (5x - 12) = 180$$

Step3: Simplify and solve for $x$

$$6x - 12 = 180$$
$$6x = 192$$
$$x = 32$$

Step4: Calculate $m\angle 2$

Substitute $x=32$ into $m\angle 2 = 5x - 12$:
$$m\angle 2 = 5(32) - 12$$

Answer:

$148^\circ$