Question

in the given figure ABCD is a square a line segment ae intersect at O such that angle aob is equal to 60 degree find the measure of angle x​

Answer 1

Answer:

Step-by-step explanation:

Let the angles be x°...

x°+x°+60°=180°

2x°=180°-60°

x°=120°/2

x°=60°.

Thus,the angles will be 60°

Answer 2

• The measure of angle x is equal to 105° .

Correct Question :- In the given figure ABCD is a a square . A line segment AE intersect the diagonal BD at O such that angle AOB = 60 . Find the measure of x ?

Concept used :-

• All four angles of a square are equal and measure 90°.
• Diagonals of a square bisect the opposite angles .
• Exterior angle of a triangle is equal to sum of opposite interior angles .

Solution :-

from image we can see that, ABCD is given square .

So,

→ ∠ADC = 90° { Angle of square }

→ DB = Diagonal of square .

then,

→ ∠CDB = 90°/2 = 45° { Diagonal of a square bisect the opposite angle }

therefore,

→ ∠EDO = 45° ------ Equation (1)

now we have given that,

→ ∠AOB = 60°

So,

→ ∠EOD = ∠AOB { Vertically opposite angles }

→ ∠EOD = 60° ------- Equation (2)

Therefore, in ∆EOD we have,

→ ∠OEC = ∠EOD + ∠EDO { Exterior angle is equal to sum of opposite interior angles }

putting values from Equation (1) and Equation (2) in RHS,

→ ∠x = 60° + 45°

→ ∠x = 105° (Ans.)

Hence, the measure of angle x is equal to 105° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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