 Krishna
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Step 1: Under stand the question and observe the given figure

Step 2: Recall properties of isosceles triangle

NOTE: Isosceles triangle has two equal sides and two equal angles.

Step 3: Find all the unknown interior angles of the isosceles triangles ABC

Skill 1: Know about  the interior angle of isosceles triangles.

NOTE: Sum of the interior angles of the isosceles triangle =

2 * (equal angle) + angle = 180 \degree

we have two equal angle.

Skill 2: Set up an equation equating 180 \degree

EXAMPLE: \triangle ABC is an isosceles triangle and

therefore  \angle CAB = \angle ABC

$\angle CAB + \angle ABC + \angle ACB = 180 \degree$

Skill 3: Substitute the known angle and simplify for the unknown angles

EXAMPLE:  $2 (\angle CAB or \angle ABC) = 180 \degree - 66 \degree$

$2 (\angle CAB or \angle ABC) = 113 \degree$

\angle CAB = \angle ABC = $\frac{113}{2} = 57 \degree$

Step 4: Follow the same process to find the unknown angles of right isosceles triangles(BCD)

NOTE: It is a right  isosceles triangles(BCD) \angle BCD = 90

EXAMPLE: \angle CBD = \angle CDB = \frac{180 - 90}{2}

$\angle CBD = \angle CDB = 45 \degree$

Step 5: Find the all angles of the right \triangle BDE

1) \triangle BDE    is a right angle so \angle BED = 90

2) Find the \angle DBE =  ?

NOTE: \angle ABC, \angle CBD and \angle DBE make a straight line

Hence   \angle ABC  + \angle CBD +   \angle DBE  = 180

Gives   \angle DBE   = 180 \degree  - ( \angle ABC  + \angle CBD )

\angle DBE = 180 \degree  - 102 \degree  = 78 \degree

3)  Find  the \angle BDE

NOTE: Sum of the angles in triangle = 180

So   \angle BED +   \angle DBE + \angle BDE = 180

\angle BDE   = 180 \degree  - (90 \degree  + 78 \degree)

\angle BDE = 12 \degree