Question

1. in a hexagon abcdef, ∠a = x°, ∠b=(x + 20)°, ∠c = 100°, ∠d=x°, ∠e=(x + 20)°, ∠f = 100°. x = 120. m∠b = 140

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 interior angles is $(6 - 2)\times180^{\circ}=720^{\circ}$.

Step2: Set up an equation

We have $x+(x + 20)+100+100+(x + 20)+x=720$.
Combining like - terms, we get $4x+240 = 720$.

Step3: Solve the equation for $x$

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

Step4: Find the measure of $\angle B$

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

Answer:

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