Question

please answer the image

Answer 1

Answer:

Given

ABC is Isosceles triangle

AB = AC

∠ABC = ∠ACB = 52' [  Angles opposite to equal sides of a triangle are equal ]

∠ACB = ∠BCE = 52'

C] 52'

Answer 2

• Value of x is 104°.

Step-by-step explanation:

If ABC is an isosceles triangle.

Then, AB = AC [Two sides of isosceles triangle are equal.]

Opposite angles of AB and AC are also equal. because if two sides of triangle are equal then, their opposite angles are equal.

Opposite angle of side AB is ∠ACB and opposite angle of AC is ∠ABC.

So,

$\sf \bold{ \angle ABC = \angle ACB}$

$\pink{ \boxed{ \sf \therefore \angle ACB = 52 \degree} \star }$

If, AB || DC

We know,

Sum of two interior angles forms on same sides side of transversal when two parallel lines interest by transversal is 180°.

Here, AB and DC are two parallel lines and BC is a transversal.

So,

$\sf \leadsto \angle ABC + \angle BCD = 180 \degree \\ \\ \sf \leadsto 52 \degree + \angle BCD = 180 \degree \\ \\ \sf \leadsto \angle BCD = 180 \degree - 52 \degree \\ \\ \sf \leadsto \boxed{\sf \bold{\angle BCD = 128 \degree}\star}$

Now,

$\sf \leadsto \angle ACD = \angle BCD - \angle ACB \\ \\ \sf \leadsto \angle ACD = 128 \degree - 52 \degree \\ \\ \sf \leadsto \boxed{\sf \bold{\angle ACD = 76 \degree} \star }$

$\sf \bold{AE \: is \: a \: straight \: line.}$

We know,

Sum of all angles forms on straight line is equal to 180°. This statement is known as $\blue{\sf \bold{ linear \: pair }}$

So,

$\sf \leadsto \angle ACD + x = 180 \degree \\ \\ \sf \leadsto 76 \degree + x = 180 \degree \\ \\ \sf \leadsto x = 180 \degree + 76 \degree \\ \\ \sf \leadsto \red{\boxed{ \sf \bold{ x = 104 \degree}} \bigstar}$

Therefore,

Value of x is 104°.