Question

Find the angle measure x in the following figure.

Answer 1

first obtain the two angle s of quadrilateral the angles are 120° and 110° .Then calculate the both angles by angle sum property.

30°+120°+110°+ x + x= 360°

260°+ 2x =360°

2x = 100°

x=50°

both x are equal because opposite angles of quadrilateral are equal so, x= 50° both.

Answer 2

[Refer to the attachment for better understanding.]

Given

• ∠BAC = 30°
• ∠BDP = 70°
• ∠CEQ = 60°
• ∠ABD = ∠ACE = x

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To Find

• The measure of 'x'.

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Solution

⇒ ∠BDP + ∠BDE = 180°  [Linear Pair]

⇒ 70° + ∠BDE = 180°

⇒ ∠BDE = 180° - 70°

⇒ ∠BDE = 110°

From the figure,

⇒ ∠CEQ + ∠CED = 180°  [Linear Pair]

⇒ 60° + ∠CED = 180°

⇒ ∠CED = 180° - 60°

⇒ ∠CED = 120°

Using the angle sum property of pentagon,

Angle Sum Property of Pentagon states that the sum of all angles in a pentagon is 540°

⇒ ∠BAC + ∠ACE + ∠CED + ∠BDE + ∠ABD = 540°

⇒ 30° + x + 120° + 110° + x = 540°

⇒ (x + x) + (30° + 120° + 110°) = 540°

⇒ 2x + 260° = 540°

⇒ 2x = 540° - 260°

⇒ 2x = 280°

⇒ x = 280/2

⇒ x = 140°

∴ The measure of 'x' is 140° in the following figure.

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