Question

ABCD is a kite L. if angle BCD=40,find angle BDC and angle ABC​

Answer 1

Answer:

Step-by-step explanation:

bcd 40

abc 50

Answer 2

Properties of kite

1) Diagonals are perpendicular.

2) 2 pairs of consecutive equal sides.

3) Vertex angles are bisects by diagonals & non vertex angles are congruent to each other

4) Diagonal between non vertex angles are bisected by vertex angle diagonal.

Given : $\angle{BCD} = 40$

To Find : $\angle{BDC} \: , \: \angle{ABC}$

Solution :

In triangle BDC

$\angle{DBC} \: = \: \angle{BDC} \: = \: x$

$\angle{DBC}\: + \: \angle{BDC} \: + \: \angle{BCD} \: = \: 180$

x + x + 40 = 180

2x = 140

x = 70

In $\triangle{ABC}$ & $\triangle{ADC}$

AB = AD ---- { by property reference no. 2 of kite}

BC = DC --- { by property reference nom 2 of kite}

AC = AC --- { Common }

$\triangle{ABC}\cong\triangle{ADC}$

$\angle{BAC} \: = \: \angle{ACD}$ by cpct

$\angle{BAC} \: = \: \dfrac{1}{2}.\angle{BCD}$

$\angle{BAC} \: = \: 20$

In ∆ AOB

$\angle{BAO}$ = 20 , $\angle{AOB}$ = 90

20 + 90 + $\angle{ABO}$ = 180

110 + $\angle{ABO}$= 180

$\angle{ABO}$ = 70

$\angle{ABC} \: = \: \angle{ABO} \: + \: \angle{DBC}$

$\angle{ABC} \: = \: 70\: + \: 70$

$\angle{ABC} \: = \: 140°$

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