Question

the measure of ∠ABC is 80°
but how???​

Answer 1

Answer:

The ∠ABC = 80° , because ΔABC is an isosceles triangle.

∴ ∠ABC = ∠ACB ( opp. ∠ of equal sides are equal )

Step-by-step explanation:

Answer 2

Note :-

Refer to the attachment for a better understanding of the answer .

$\bold\color{plum} {Solution :- }$

Given :-

∠ABC = 80°

Reason :-

As the exterior angle = ∠100° and ∠C are a linear pair which means their sum will be equal to 180° .

Since ∠ABC and ∠ACB are the alternate base angles of an isosceles triangle , their value will be equal . That is why the value of ∠ACB :-

$\color{hotpink}= 80°$

So :-

$∠100 + ∠C = 180°$

So ∠ACB = 80°

As the base angles of this triangle I.e, ∠ABC and ∠ACB are equal , this triangle must be an isosceles triangle.

As , the base angles add up to (80° + 80° = 160° ) , the third angle , which is ∠BAC must be of the measure 20° , according to the angle sum property which says that the three angles of a triangle add upto 180° .

Therefore , ∠ABC = 80° because it's alternate base angle ( ∠ACB ) is also equal to 80° . As this triangle is an isosceles triangle, the value of their opposite base angles will be equal , that is why we say :-

$\bold\color{olive}∠ABC = 80° = \bold \color{hotpink} ∠ACB = 80°$