Question

In an isosceles triangle the base angle are equal .The vertex angle is 14degree .What are the base angle of the triangle ( Remember the sum of three angles of a triangle is 180 degree

Answer 1

Given:

The base angles of an isosceles triangle are same. And third angle of the triangle is 14°.

To be found:

The base angles

So,

We know that

$\boxed{\bf{Angle\:\:sum\:\:property:- }} \\ \\ \boxed{\boxed{\sf{Sum\:\:of\:\:all\:\:three\:\:angles \:\:of\:\:triangle= 180^{o} }}}$

Now,

Let the base angles be x. [Both will be x, as both are same]

→ x + x + 14 = 180

→ 2x + 14 = 180

→ 2x = 180 - 14

→ 2x = 166

→ x = 166 ÷ 2

→ x = 83

So, the angles of the base of triangle = x = 83°

$\bf{\underline{\underline{Verification:-}}}$

83° + 83° + 14°

= 166° + 14°

= 180°

Answer 2

Answer:

Given:

• In an isosceles triangle the base angle are equal. The vertex angle is 14°.

Find:

• What are the base angle of the triangle.

Using Angle sum property:

☆ ${\sf{\underline{\boxed{\red{\sf{ Sum \: of \: all \: three \: triangles = 180°}}}}}}$

Calculations:

• Let x be the base angles and the common variable to this question.

⇒ $\sf{x + x + 14 = 180}$

⇒ $\sf{2x + 14 = 180}$

⇒ $\sf{2x = 180 - 14}$

⇒ $\sf{2x = 166}$

⇒ $\sf{x= 166 ÷ 2}$

⇒ ${\sf{\underline{\boxed{\red{\sf{x = 83° }}}}}}$

Therefore, the two bases angles are (83° + 83°) = 166°

VERIFICATION:

• We know that the sum of all three angles = 180°

⇒ $\sf{83° + 83° + 14°}$

⇒ ${\sf{\underline{\boxed{\red{\sf{180° }}}}}}$

HENCE PROVED!!!