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

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

Answer 2

Answer:

$36^{\circ}$

Step-by-step 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

$3x+2x=180^{\circ}$

$5x=180^{\circ}$

$x=\frac{180}{5}=36^{\circ}$

Hence, the size of angle C=$36^{\circ}$