Find the angle measure `x` in the following figures

Explanation

(a) The given figure has 4
sides and hence it is a quadrilateral
Find the angle measure x
Using the angle sum property of a quadrilateral,
`50^@ + 130^@ + 120^@ +x=360^@ `
`300^@ + x = 360^@ `
`x = 360^@ - 300^@ `
`x = 60^@ `
(b) Usingtheanglesum
property of a quadrilateral.
Find the angle measurexin
the following figures:
The line is perpendicular to
the base line hence, the angle formed is 90°.
`90^@ + 60^@ + 70^@ + x = 360^@ `
`220^@ + x = 360^@ `
`220^@ + x = 360^@ `
`x = 360^@ - 220^@ `
`x = 140^@ `

(c) The given figure is a pentagon (number of sides =5)
Find the angle measure x in the following figures:
Angle sum of a polygon = `(n - 2) × 180^@`
`= (5 - 2) × 180^@ `
`= 3 × 180^@ `
`= 540^@ `
Sum of the interior angle of pentagon is 540^@ .
Angles at the bottom are linear pairs.

Thus, First base interior angle,
= 180^@ - 70^@ (angle of straight line is 180° )
`= 110^@ `
Also, Second base interior angle,
`= 180^@ - 60^@ `

`= 120^@ `
Angle sum property of a polygon = (n - 2) × 180^@
`⇒ 30^@ + x + 110^@ + 120° + x = 540^@ `
`⇒ 2x + 260^@ = 540^@ `
`⇒ 2x = 540^@ - 260^@ `
`⇒ 2x = 280^@ `
`⇒ x =( 280^@ )/2`
Therefore, x = `140^@ `
(d) The given figure is pentagon (number of sides =5)
Find the angle measure x in the following figures:
Sum of the interior angle of pentagon is 540^@
Angle sum of a polygon`= (n - 2) × 180^@ `
`= (5 - 2) × 180^@ `
`= 3 × 180^@ `
`= 540^@ `
Let each angle of the polygon be x since it is a regular pentagon
Angle sum of a polygon =` x + x + x + x + x = 540^@ `
`5x = 540^@ `
`x =( 540^@ )/5`
`x = 108^@ `
The givenpentagonisa
regular polygoni.e.itisboth‘equilateral’ and
‘equiangular’. Thus, the measure of each interior
angle of the pentagon is equal.
Hence each interior angle is `108^@ `