Q. 265.0( 1 Vote )

# In a rhombus ABCD, if ∠ACB =40°, then ∠ADB =

A. 70°

B. 45°

C. 50°

D. 60°

Answer :

The diagonals in a rhombus are perpendicular,

So,

∠BPC = 90^{o}

From triangle BPC,

The sum of angles is 180°

So,

∠CBP = 180^{o} – 40^{o} – 90^{o}

= 50°

Since, triangle ABC is isosceles

We have,

AB = BC

So,

∠ACB = ∠CAB = 40^{o}

Again from triangle APB,

∠PBA = 180^{o} – 40^{o} – 90^{o}

= 50^{o}

Again, triangle ADB is isosceles,

So,

∠ADB = ∠DBA = 50^{o}

∠ADB = 50^{o}

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