Question

(4 points)

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

$m\angle 2=$
(4 points)

1. if $l \parallel m$, find the values of x and y.

$(7x + 12)^\circ$
$(12x - 28)^\circ$
$(9y - 77)^\circ$
$x =$
$y =$

Explanation:

Problem 8

Step1: Define linear pair relation

A linear pair sums to $180^\circ$, so $m\angle1 + m\angle2 = 180^\circ$.

Step2: Translate given condition

Given $m\angle2 = 5m\angle1 - 12$. Substitute into the equation:
$m\angle1 + (5m\angle1 - 12) = 180$

Step3: Solve for $m\angle1$

Combine like terms: $6m\angle1 - 12 = 180$
Add 12 to both sides: $6m\angle1 = 192$
Divide by 6: $m\angle1 = 32$

Step4: Calculate $m\angle2$

Substitute $m\angle1=32$ into $m\angle2 = 5m\angle1 - 12$:
$m\angle2 = 5(32) - 12 = 160 - 12$

Step1: Set up equation for $x$

Corresponding angles are equal: $7x + 12 = 12x - 28$

Step2: Solve for $x$

Rearrange terms: $12 + 28 = 12x - 7x$
Simplify: $40 = 5x$
Divide by 5: $x = 8$

Step3: Set up equation for $y$

Same-side interior angles sum to $180^\circ$: $(12x - 28) + (9y - 77) = 180$

Step4: Substitute $x=8$ and solve for $y$

First calculate $12(8)-28 = 96-28=68$
Substitute into the equation: $68 + 9y - 77 = 180$
Simplify: $9y - 9 = 180$
Add 9 to both sides: $9y = 189$
Divide by 9: $y = 21$

Answer:

$m\angle2 = 148$

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Problem 9