# Find the measure of each angle of a parallelogram, if one of its angles is 30^{o} less than twice the smallest angle.

### Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

### Let the smallest angle be x.
Then one of the angles is 2x – 30^{o}
(2x – 30^{o}) + x = 180^{o}
(Interior angles on same side of transversal are supplementary)
_{} x = 70^{o}
One angle = (2x – 30^{o}) = 110^{o}
Opposite angles of a parallelogram are equal
Hence, the four angles are 70^{o}, 110^{o}, 70^{o}, 110^{o}

^{o}

^{o}) + x = 180

^{o}

_{}x = 70

^{o}

^{o}) = 110

^{o}

^{o}, 110

^{o}, 70

^{o}, 110

^{o}

### Answered by | 4th Jun, 2014, 03:23: PM

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