Question

In figure,ABC is an equilateral triangle BDC is an isosceles right triangle,right angled at D angle ABD equal to___​

Answer 1

Answer:

105°

REFER TO THE PHOTO ☝️☝️

Answer 2

The answer is 105°

GIVEN

• ABC is an equilateral triangle
• BDC is an isosceles triangle
• ∠BDC = 90°

TO FIND

∠ABD

SOLUTION

We can simply solve the above problem as follows;

It is given

ΔABC is an equilateral triangle.

We know that,

∠ABD = ∠ABC + ∠DBC

Now,

All sides of an equilateral traingle are equal to one another,

Therefore,

AB = BC =CA

And,

All angles of an equilateral triangle are equal to 60°

Therefore,

∠ABC = 60° (Equation 1)

In ΔBDC

BD = DC (GIVEN)

∠BDC = 90° (GIVEN)

∠DBC = ∠DCB (Equal angles of equal sides)

Therefore,

∠BDC + ∠DBC + ∠DCB = 180° (Sum of interior angle of triangle is 180°)

90° + 2∠DBC = 180°

2∠DBC = 90

∠DBC = 90/2 = 45° (EQUATION 2)

Now,

(Equation 1) + (Equation 2)

∠ABD = 45 + 60 = 105°

Hence, The answer is 105°

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