Question

In the figure at right, it is given than BDC is straight, BD = DA, and AB = AC = DC. Find the size of angle C

Answer 1

`36^(\circ)`

Explanation:

We are given that BDC is straight.

BD=DA

AB=AC=DC

Let
`m\angle B=x`

Then,
`m\angle B=m\angle C=x`

Because AB=AC, angle made by two equal sides are equal.

Let
`m\angle ADC=y=m\angle CAD`

`m\angle A=m\angle BAD+m\angle CAD`

`m\angle BAD=m\angle B`

`m\angle A=x+y`

In triangle ABC

`m\angle B+m\angle A+m\angle C=180^(\circ)` sum of angles of triangle

`x+x+y+x=180^(\circ)`

`3x+y=180^(\circ)`

`m\angle ADC=m\angle B+m\angle BAD=x+x=2x`

Exterior angle is equal to sum of two interior angles on the opposite side.

Substitute the values then we get

`3x+2x=180^(\circ)`

`5x=180^(\circ)`

`x=(180)/(5)=36^(\circ)`

Hence, the size of angle C=
`36^(\circ)`

Answer 2

you need to use the angle sum of a triangle in triangle CAD to express y in term of x
for triangla CAD , y = (180 -x) /2
180 = 3x + [ (180-x)/2]

x = 36

hope this helps