Question

6. ABCD is a kite and A = C. If CAD = 60° and CBD = 45°,find
1=BCD
2=CDA​

Answer 1

Step-by-step explanation:

Given: Angle ACD=CAD=60°, angle CBD=45°.

(I). Let the Intersecting point of diagnosis be O

We know that: One of the diagonals of a kite is the perpendicular bisector of the other,

So, angle BOC=90°.

Consider ∆BOC,

B+C+O=180°.

45°+90°+C=180°(Sum of interior angle of triangle=180°)

C=180°-135°

angle BCA=45°.

=> Angle BCD= angle BCA+ angle ACD

=> 45°+60°

=> 105°.

(ii).Angle BCD=BAD=105°, Angle ABC=90°.

[Sum of interior angles of a quadrilateral=360°]

105°+105°+90°+ADC=360°

ADC=360°-300°

Angle ADC=60°.