Question

1. ∠abc and ∠def are supplementary angles.

(7x - 46)°
(3x + 6)°
______ = x
______ = m∠abc
______ = m∠def

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles sum to 180°. So, $(7x - 46)+(3x + 6)=180$.

Step2: Simplify the left - hand side

Combine like terms: $7x+3x-46 + 6=180$, which simplifies to $10x-40 = 180$.

Step3: Isolate the variable term

Add 40 to both sides of the equation: $10x-40 + 40=180 + 40$, resulting in $10x=220$.

Step4: Solve for x

Divide both sides by 10: $\frac{10x}{10}=\frac{220}{10}$, so $x = 22$.

Step5: Find $m\angle ABC$

Substitute $x = 22$ into the expression for $\angle ABC$: $m\angle ABC=7x-46=7\times22-46=154 - 46=108$.

Step6: Find $m\angle DEF$

Substitute $x = 22$ into the expression for $\angle DEF$: $m\angle DEF=3x + 6=3\times22+6=66 + 6=72$.

Answer:

$x = 22$
$m\angle ABC=108^{\circ}$
$m\angle DEF=72^{\circ}$