Question

Given that abc is an isosceles triangle and ad and cd are angle bisectors what is m

Answer 1

Answer:

Angle ADC = 116°

Step-by-step explanation:

180-52 = 128

128/2 = 64

Since both angles a and b equal 64 there no sense in half then doubling.

180-64 = 116°

Answer 2

Applying the definition of an isosceles triangle, the measure of angle ADC in the diagram given will be: 116 degrees.

Recall:

• There are two base angles in an isosceles triangle that are congruent to each other.
• An angle bisector divides an angle into two equal halves.
• Sum of triangle = 180 degrees.

Given that triangle ABC is an isosceles triangle, therefore:

<BAC = <BCA (base angles)

Thus,

m<BAC = (180 - 52)/2

m<BAC = 64 degrees

m< BAC = m<BCA = 64 degrees.

Since CD and AD bisects <BAC and <BCA, therefore,

m<DAC = 64/2 = 32 degrees

m<DCA = 64/2 = 32 degrees

• Thus:

m<ADC = 180 - (m<DAC + m<DCA) (sum of triangle)

• Substitute:

m<ADC = 180 - (32 + 32)

m<ADC = 116 degrees.

Therefore, applying the definition of an isosceles triangle, the measure of angle ADC in the diagram given will be: 116 degrees.

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