Question

In the adjoining figure, ABCD is a rhombus . If angle A=70°, find angle CDB​

Answer 1

AD =AB (adjacent sides of a rhombus are equal)

therefore angle ABD =angle ADB(angles opposite equal sides are equal)

let angle ABD=angleADB=x(say)

in triangle ABD we have,

70+x+x=180

70+2x=180

2x=180-70

2x=110

x=55

therefore angleABD=angleADB=55 degree

angle ABD=angle CDB (alternate angles)

therefore angle CDB=55 degree

Answer 2

Answer:

☯️ Given ☯️

• $\mapsto$ In the adjoining figure, ABCD is a rhombus. If angle A = 70°.

☯️ To Find ☯️

• $\mapsto$ What is the angle of CDB.

☯️ Solution ☯️

➕ In ∆ CBA ,

$\implies$ $\angle$BCA = $\angle$ BAC = 35°

$\implies$ $\angle$CBA = 180° - 2 × 35 = 110°

$\implies$ $\angle$CDA + $\angle$CBA = 360° - 2 × $\angle$DAB [Since $\angle$BCD = $\angle$BAD, is a rhombus]

$\implies$ 360° - 2 × 70°

$\longrightarrow$ 220°

✴️ $\angle$CDA = $\angle$CBA = $\sf\dfrac{\cancel{220}}{\cancel{2}}$ = 110°

➡️ Diagonals in a rhombus are angle bisectors.

$\longrightarrow$ $\angle$CDB = $\sf\dfrac{\cancel{110}}{\cancel{2}}$ = 55°.

$\therefore$ The angle of CDB is 55°.

Step-by-step explanation:

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