Question

In the figure abc is an isosceles triangle with ab=ac and angle a=50° ;b is eQual to. (A)130
(b)50 (c)40 (d)65

Answer 1

Answer :

The Angle B = 40°

Option => D

Explanation :

Given that,

∆ABC is an isoceles triangle .

◾AB = AC .

◾Measure of Angle A = 50°

★ Consider as -

◾The Angle A & B as - x.

We know that :

The base angles of an Isosceles triangle are Same, Equal.

So,

We also know that :

The sum of the angles of a triangle is 180°

So,

$\boxed{\sf A + B + C = 180\textdegree}}$

Now,

$\sf \\\implies 50 +x+x = 180\\ \\\implies 50 + 2x = 180\\ \\\implies 2x = 180-50\\ \\\implies x = \dfrac{130}{2}\\ \\\implies x = 65$

Hence,

The angle B is equal to 65° (Option => D)

$\rule{300}{1.5}$

★ Points to Remember -

◾The base angles of an Isosceles triangle are Same, Equal.

◾The sum of the angles of a triangle is 180°

★ Pythagorean theorem -

◾The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

◾We can write it as -

$\bigstar\;\boxed{\sf H^2 = P^2 + B^2}}$