Question

In the above figure, ABCD is a rhombus. If angle BAC =32 degree, find


Angle ACB

Angle DAC

Angle ADC ​

Answer 1

Angles of Rhombus

Answer: ∠ACB = 32° , ∠DAC = 32° and ∠ADC = 116°.

Explanation:

Given that ∠BAC = 32° .

Need to determine ∠ACB , ∠DAC and ∠ADC.

lets first go through on of the important property of rhombus whic says that "OPPOSITE ANGLE OF RHOMBUS ARE EQUAL"

using above property we can say that ∠A = ∠C

=> (1/2)∠A  = (1/2)∠C         ------Eq(1)

Another Important Property of RHOMBUS is "DIAGONAL OF RHOMBUS BISECTS ANGLES AT ITS END"

=> AC bisects ∠A  and CA bisects ∠C

=> ∠DAC = ∠BAC =  1/2(∠A) = 32° and ∠ACB = ∠ACD =  1/2(∠C)

using equation 1  1/2(∠C)  = 1/2(∠A) = 32°

=> ∠ACB = ∠ACD =  1/2(∠C)  = 32°

So now we have ∠DAC = ∠BAC =  ∠ACB = ∠ACD = 32°

Now consider ΔADC.

using ANGLE SUM PROPERTY OF TRIANGLE , we can say that

∠DAC + ∠ACD + ∠ADC = 180°

=> 32° + 32° + ∠ADC = 180°     [ since ∠DAC = ∠ACD = 32° ]

=> ∠ADC = 180° - 32° - 32°

=> ∠ADC = 180° - 64°

=> ∠ADC = 116°

Hence summarizing our findings we get ∠ACB = 32° , ∠DAC = 32° and ∠ADC = 116°.

#answerwithquality

#BAL