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

One angles of...

Question

One angles of an isosceles triangle is 120°. What are the other two angles?

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Solution

Given: An isosceles triangle ABC with ∠BAC = 120°.

We know that in an isosceles triangle, two sides are of equal length.

In ΔABC, AB = AC

Also, angles opposite to equal sides of an isosceles triangle are equal.

⇒∠ACB = ∠ABC

Using angle sum property in ΔABC, we have:

∠ABC + ∠BCA + ∠CAB = 180°

⇒ 2∠ABC + 120° = 180°

⇒ 2∠ABC = 180° − 120°

⇒ ∠ABC = = 30°

Thus, the other two angles of the triangle are of measures 30° each.

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