Question

one of the base angle of an isosceles triangle is 70°. The vertical angle is:
40° or 80°


need full explaination​

Answer 1

Answer :-

• The vertical angle of the isosceles triangle = 40°.

Given :-

• One of the base angles of an isosceles triangle is 70°.

To find :-

• The vertical angle.

Step-by-step explanation :-

It has been given that one of the base angles of an isosceles triangle is 70°.

We know that in an isosceles triangle, the base angles are equal.

So, that means the other base angle is 70° too.

Let the vertical angle be x.

Now,

$\underline{\boxed{\sf Sum \: of \: all \: the \: angles \: in \: a \: triangle = 180^{\circ}}}$

So, all these angles must add up to 180°.

$\tt \implies70^{\circ} + 70^{\circ} + x = 180^{\circ}.$

Adding the numbers,

$\tt \implies140^{\circ} + x = 180^{\circ}.$

Transposing 140° from LHS to RHS, changing it's sign,

$\tt\implies x = 180^{\circ} - 140^{\circ}$

Subtracting the numbers,

$\tt \implies x = 40^{\circ}.$

• The value of x = 40°.

-----------------------------------------------------------

• Hence, the vertical angle = 40°.

Answer 2

❍ One of the Base of angle of an isosceles triangle is 70⁰ .

As We know that ,

⠀⠀⠀⠀⠀According To Properties of Isosceles :

• The base angles of an Isosceles triangle is always equal .

Therefore,

• Angle 2 of an Isosceles triangle is 70⁰ .

❍ Let's Consider the vertical angle of na Isosceles triangle be x .

$\underline{\pink{\bigstar\:\boldsymbol{By\: Using\; ASP \; Property\::}}}$

• Angle Sum Property of Triangle is basically, sum of all angles of the triangle is 180°.

Therefore,

$\dashrightarrow\sf 70 + 70 + x = 180^\circ \\\\\\\dashrightarrow\sf 140 + x = 180^\circ \\\\\\\dashrightarrow\sf x = 180^\circ - 140^\circ \\\\\\\dashrightarrow{\underline{\boxed{\frak{\pink{x = 40^\circ}}}}}$

$\therefore{\underline{\sf{Hence,\;Vertical\:angle\;of\;the\;\triangle\;is\; \bf{40^\circ}.}}}$

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