Question

find m∠1 and m∠2. justify each answer. 12. 13. 14. algebra find the value of x. then f

Explanation:

Step1: Identify angle - relationship in 12

In problem 12, $\angle1$ and the $75^{\circ}$ angle are corresponding angles. Since $\ell\parallel m$ and $t$ is a transversal, corresponding angles are congruent.
$m\angle1 = 75^{\circ}$

Step2: Identify angle - relationship for $\angle2$ in 12

$\angle2$ and the $75^{\circ}$ angle are alternate - interior angles. Since $\ell\parallel m$ and $t$ is a transversal, alternate - interior angles are congruent.
$m\angle2=75^{\circ}$

Step3: Identify angle - relationship in 13

In problem 13, the angle adjacent to the $120^{\circ}$ angle forms a linear pair with it. So, the measure of the adjacent angle is $180 - 120=60^{\circ}$. $\angle1$ and this adjacent angle are corresponding angles. Since $a\parallel b$ and $q$ is a transversal, corresponding angles are congruent.
$m\angle1 = 60^{\circ}$

Step4: Identify angle - relationship for $\angle2$ in 13

$\angle2$ and the $120^{\circ}$ angle are alternate - exterior angles. Since $a\parallel b$ and $q$ is a transversal, alternate - exterior angles are congruent.
$m\angle2 = 120^{\circ}$

Step5: Identify angle - relationship in 14

In problem 14, the sum of the interior angles of a quadrilateral is $360^{\circ}$.
We know two angles are $80^{\circ}$ and $70^{\circ}$. Let's find $m\angle1$ and $m\angle2$.
The angle adjacent to the $80^{\circ}$ angle and $\angle1$ are supplementary (linear - pair), so the adjacent angle to $80^{\circ}$ is $100^{\circ}$. The angle adjacent to the $70^{\circ}$ angle is $110^{\circ}$.
$m\angle1=100^{\circ}$ and $m\angle2 = 110^{\circ}$

Answer:

In problem 12: $m\angle1 = 75^{\circ}$, $m\angle2 = 75^{\circ}$
In problem 13: $m\angle1 = 60^{\circ}$, $m\angle2 = 120^{\circ}$
In problem 14: $m\angle1 = 100^{\circ}$, $m\angle2 = 110^{\circ}$