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r-ruslan [8.4K]
3 years ago
8

Please help if you can thanks ^^

Mathematics
1 answer:
Neko [114]3 years ago
3 0

Given:

AD is an angle bisector in triangle ABC. m\angle CAB=44^\circ, m\angle ACB=72^\circ, m\angle ABC=64^\circ.

To find:

The value of m\angle ADC.

Solution:

AD is an angle bisector in triangle ABC.

m\angle CAD=m\angle BAD=\dfrac{m\angle CAB}{2}

m\angle CAD=m\angle BAD=\dfrac{44^\circ}{2}

m\angle CAD=m\angle BAD=22^\circ

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

Using angle sum property in triangle CAD, we get

m\angle CAD+m\angle ADC+m\angle ACB=180^\circ

22^\circ+m\angle ADC+72^\circ=180^\circ

m\angle ADC+94^\circ=180^\circ

m\angle ADC=180^\circ-94^\circ

m\angle ADC=86^\circ

Therefore, the angle of angle ADC is 86^\circ.

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