Question

7. Find the angle measure x in each of the following figures:
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Answer 1

80 degree is the answer

Answer 2

GIVEN :-

◉ For First Figure Through Attachment,

• ∠BAX = 125°.
• ∠CBY = 125°.
• ∠ACZ = x°.

◉ For second Figure Through Attachment,

• ∠BAP = 90°.
• ∠CBQ = 90°.
• ∠DCR = x°.
• ∠AET = 60°.
• ∠EDS = 1 (Assumed).

TO FIND :-

• The value of x in both the figure .

SOLUTION :-

◉ For First Figure,

As we know that the sum of exterior angles of any closed figure is 360°.

∴ ∠BAX + ∠CBY + ∠ACZ = 360°.

➺ 125° + 125° + x = 360°

➺ 250° + x = 360°

➺ x = 360° - 250°

➺ x = 110°.

❏ Hence the value of x in First Figure is 110°.

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◉ For second Figure,

➔ ∠EDS + ∠EDC = 180° [Linear pair]

➔ ∠1 + 90° = 180°

➔∠1 = 180° - 90°

➔∠1 = 90°.

As we know that the sum of exterior angles of any closed figure is 360°.

∴∠BAP+∠CBQ+∠DCR+∠EDS+∠AET = 360°

➺ 90° + 70° + x + 90° + 60° = 360°

➺ 310° + x = 360°

➺ x = 360° - 310°

➺ x = 50°

❏ Hence the value of x in second Figure is 50°