Question

(b) The vertical angle of an isosceles triangle is 80°. Find measurement of its base
angles.
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Answer 1

Correct Question :-

• The vertical angle of an isosceles triangle is 80°. Find the measurement of its base angles.

Answer :-

• The measurement of the base angles is 50°.

To find :-

• The measurement of the base angles of the isosceles triangle.

Step-by-step explanation :-

• Here, it is given that the vertical angle of an isosceles triangle is 80°. We have to find the measurement of it's base angles.

We know that :-

• An isosceles triangle has two equal base angles.

Let :-

• The base angles be "x" and "x".

Now, we know that :-

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

Here,

• Vertical angle = 80°.
• Base angles = x and x.

Therefore,

$\mapsto \sf{x + x + 80 = 180}$

$\mapsto \sf{x + x = 180 - 80}$

$\mapsto \sf{x + x = 100}$

$\mapsto \sf{2x = 100}$

$\mapsto \sf{x = \cancel{\dfrac{100}{2}}}$

$\mapsto \sf{x = 50}$

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Hence, the angles are :-

$\longmapsto \bf{x = {50}^{\circ}}$

$\longmapsto \bf{x = {50}^{\circ}}$

Thus :-

• The two base angles of the isosceles triangle are 50° and 50°.

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