Question

1. if ∠1 and ∠2 form a linear pair, find the measure of both angles if the m∠2 is 33 less than twice the m∠1.

Explanation:

Step1: Recall linear - pair property

Linear - pair angles add up to 180 degrees. So, $m\angle1 + m\angle2=180^{\circ}$.

Step2: Set up an equation based on the given relationship

We are given that $m\angle2 = 2m\angle1- 33$.

Step3: Substitute the expression for $m\angle2$ into the linear - pair equation

Substitute $m\angle2$ in $m\angle1 + m\angle2 = 180$:
$m\angle1+(2m\angle1 - 33)=180$.

Step4: Simplify the left - hand side of the equation

Combine like terms: $m\angle1+2m\angle1-33 = 3m\angle1-33$. So, $3m\angle1-33 = 180$.

Step5: Solve for $m\angle1$

Add 33 to both sides of the equation: $3m\angle1=180 + 33=213$. Then divide both sides by 3: $m\angle1=\frac{213}{3}=71^{\circ}$.

Step6: Solve for $m\angle2$

Substitute $m\angle1 = 71$ into the equation $m\angle2 = 2m\angle1-33$. Then $m\angle2=2\times71-33=142 - 33 = 109^{\circ}$.

Answer:

$m\angle1 = 71^{\circ}$, $m\angle2 = 109^{\circ}$