Two adjacent angles of a parallelogram are the ration 2:3. Find the me

1.	Two adjacent angles of a parallelogram are the ration 2:3. Find the measure of each of its angles.
Answer» \(\angle A=72^\circ\), \(\angle B=108^\circ\), \(\angle C=72^\circ\), \(\angle D=108^\circ\) Let x be the common multiple. As per question, \(\angle A\) = 2x \(\angle B\) = 3x \(\angle C\) = 2x \(\angle D\) = 3x \(\angle A\) + \(\angle B\) = 180° (Adjacent angles of parallelogram is supplementary) 2x + 3x = 180° 5x = 180° X = 180 / 5 = 36° \(\angle A\) = 2 × 36° = 72° \(\angle B\) = 3 × 36° = 108° \(\angle C\) = 2 × 36° = 72° \(\angle D\) = 3 × 36° = 108° So, Angles of quadrilateral are 72°, 108°, 72° and 108°.

Two adjacent angles of a parallelogram are the ration 2:3. Find the measure of each of its angles.

Answer»

\(\angle A=72^\circ\), \(\angle B=108^\circ\), \(\angle C=72^\circ\), \(\angle D=108^\circ\)

Let x be the common multiple.

As per question,

\(\angle A\) = 2x

\(\angle B\) = 3x

\(\angle C\) = 2x

\(\angle D\) = 3x

\(\angle A\) + \(\angle B\) = 180° (Adjacent angles of parallelogram is supplementary)

2x + 3x = 180°

5x = 180°

X = 180 / 5 = 36°

\(\angle A\) = 2 × 36° = 72°

\(\angle B\) = 3 × 36° = 108°

\(\angle C\) = 2 × 36° = 72°

\(\angle D\) = 3 × 36° = 108°

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

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