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Construct Triangle When Its Base, Difference of the Other Two Sides and One Base Angle Are Given

One of the ba...

Question

One of the base angles of an isosceles triangle is 70°. The vertical angle is
(a) 60°
(b) 80°
(c) 40°
(d) 35°

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Solution

Correct option: (c)
Let ∠A = 70^o
The triangle is an isosceles triangle.
We know that the angles opposite to the equal sides of an isosceles triangle are equal.
$∴$ ∠B = 70^o
We need to find the vertical angle ∠C.
Now, sum of all the angles of a triangle is 180^o.
∠A + ∠B + ∠C = 180^o
⇒ 70^o + 70^o + ∠C = 180^o
⇒ 140^o+ ∠C = 180^o
⇒ ∠C = 180^o $-$ 140^o
⇒ ∠C = 40^o

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