Question

1. a b x° (x + 20)° 100° 100° c f (x + 20)° x° e d x = m∠b =

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. For a hexagon, $n=6$, so the sum of the interior angles is $(6 - 2)\times180^{\circ}=720^{\circ}$.

Step2: Set up an equation

We have the angles $x^{\circ},(x + 20)^{\circ},100^{\circ},100^{\circ},(x + 20)^{\circ},x^{\circ}$. So, $x+(x + 20)+100+100+(x + 20)+x=720$.

Step3: Combine like - terms

Combining like - terms gives $4x+240 = 720$.

Step4: Solve for $x$

Subtract 240 from both sides: $4x=720 - 240=480$. Then divide both sides by 4: $x=\frac{480}{4}=120$.

Step5: Find $m\angle B$

Since $m\angle B=(x + 20)^{\circ}$ and $x = 120$, then $m\angle B=120+20=140^{\circ}$.

Answer:

$x = 120$
$m\angle B=140$