Question

Geometry math question

Answer 1

$formulae \: for \: sum \: of \: all \: interior \: \\ angle \: of \: polygon \: is \\ (n - 2) \times 180 \\ where \: n \: is \: number \:of \: side \: of \: polygon \:$
$(5 - 2) \times 180 = 12x \\ x = 45 \\ so \: at \: vertex \: e \: angle \: is \: 3x = 135$

Answer 2

STEP 1: Find the sum of the interior angles

Sum of interior angles = (n - 2) x 180 where n is the number of sides.

Given that the figure in the picture has 5 sides,

Sum of the interior angles = (5 - 2) x 180 = 540°

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STEP 2: Find the value of x

We add up all the angles and equate it with 540°.

2x + 2x + 2x + 3x + 3x = 12x

12x = 540°

Since 12x = 540, to find 1x, we divide 540 by 12:

x = 540 ÷ 12

x = 45

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STEP 3: Find interior angle at vertex E

Angle at vertex E is 3x

Since we know that 1x = 45, to find 3x, we multiply it by 3

1x = 45

3x = 45 x 3 = 135°

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Answer: 135°