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Angle Sum Property

The angles of...

Question

The angles of an isosceles triangle are in the ratio 1 : 4 : 4. Find the measure of the base angle of the triangle.

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Solution

$\begin{matrix} L e t t h e a n g l e o f i s o s c e l e s t r i a n g l e b e x, 4 x a n d 4 x N o w, s u m o f a n g l e s o f t r i a n e = 180 \Rightarrow x + 4 x + 4 x = 180 \Rightarrow 9 x = 180 ∴ x = 20 H e n c e, 1 s t a n g l e = x = 20^{\circ} 2 n d a n g l e = 4 x = 4 \times 20^{\circ} = 80^{\circ} 3 r d a n g l e = 4 x = 4 \times 20^{\circ} = 80^{\circ} . \end{matrix}$

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