1.

The angels of a quadrilateral are in the ration 1:2:3:4. Find the measure of each angle.

Answer»

36°,72°,108°,144°

Let x be the common multiple.

As per question,

\(\angle A\) = x

\(\angle B\) = 2x

\(\angle C\) = 3x

\(\angle D\) = 4x

As we know that, Sum of all four angles of quadrilateral is 360°.

\(\angle A\) + \(\angle B\) + \(\angle C\) + \(\angle D=360^\circ\)

x + 2x + 3x + 4x = 360°

10x = 360°

X = 360/10

= 36°

\(\angle A\) = 1 X 36° = 36°

\(\angle B\) = 2 X 36° = 72°

\(\angle C\) = 3 X 36° = 108°

\(\angle D\) = 4 X 36° = 144°

So, Angles of quadrilateral are 36°, 72°, 108° and 144°.



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