Question

Rhombus ABCD has a diagonal BD¯¯¯¯¯.

m∠ADB=(4x−12)°

m∠CDB=(3x+6)°

What is the m∠ADC ?

Enter your answer in the box

º

Answer 1

As it's a rhoumbus angles are equal

• m<ADB=m<CDB
• 4x-12=3x+6
• x=18

m<ADC

• 4x-12+3x+6
• 7x-6
• 7(18)-6
• 126-6
• 120°

Answer 2

Solution given:

m∠ADB=(4x−12)°

m∠CDB=(3x+6)°

m∠ADC =?

Since diagonal BD bisect the angle <ADC

so

m∠ADB= m∠ADC

(4x-12)°=(3x+6)°

4x-3x=6-12

x=12+6

x=18°

again.

<ADB=m∠ADB+ m∠ADC=4×18-12+3×18+6=120°

So

the m∠ADC =120°