Question

Angle homework , help fasttt thanksss

Answer 1

Answer:

$\boxed{question \: number \: 4} \to \boxed{x = 36} \\ \boxed{question \: number \: 5} \to \boxed{x = 120}$

Step-by-step explanation:

$\boxed{question \: number \: 4 \to} \\ each \: interior \: angle \: \boxed{a}\: of \: a \: regular \: polygon \: is \to \\ \boxed{a = \frac{(n - 2)180}{n} }..........where \: \boxed{n} \: is \: the \: \boxed{number \: of \: sides} \\ a = \frac{(5 - 2)180}{5} = \frac{3 \times 180}{5} \\ a = 108 \to \: hence \: \to \\ \boxed {180 - both \: equal \: base \: angles \: of \: the \: triangle = x} \\ 180 - 108 = 72 \to \: angles \: on \: a \: straight \: line \\ x + 2 \times 72 = 180 \\ x = 180 - 144 \\ \boxed{x = 36.} \\ \\ \boxed{question \: number \: 5 \to} \\ each \: interior \: angle \: \boxed{a}\: of \: a \: regular \: polygon \: is \to \\ \boxed{a = \frac{(n - 2)180}{n} }..........where \: \boxed{n} \: is \: the \: \boxed{number \: of \: sides} \\ a = \frac{(6- 2)180}{6} = \frac{4 \times 120}{6} \\ a = 108 \to hence \to \\ \boxed {180 - both \: equal \: base \: angles \: of \: the \: triangle = 60} \\ 2x + 2(60) = 360 \to \: sum \: of \: angles \:at \: a \: point\\ 2x + 120 = 360 \\ 2x = 360 - 120\\ x = \frac{240}{2} \\ \boxed{x =120.}$

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