Question

if the ratio of measures of two adjacent angles of parallelogram is 1: 2 find the measures of all angles of the parallelogram​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

$\underline{\bf Given :}$

• If the ratio of measures of two adjacent angles of parallelogram is 1 : 2

$\underline{\bf To \: Find :}$

• The measures of all angles of the parallelogram

$\underline{\bf Solution :}$

Let,

• The measures of two adjacent angles of a parallelogram is '1x' and '2x'

We know that,

$\boxed{\sf The \: sum \: of \: adjacent \: angles \: of \: parallelogram \: is \: 180\degree}$

$\underline{\bf A.T.Q :}$

$\implies$1x + 2x = 180

$\implies$3x = 180

$\implies$x = (180)/3

$\implies$x = 60

$\underline{\bf Therefore :}$

The measure of two adjacent angles of parallel will be,

• 1x = 1 × 60 = 60°
• 2x = 2 × 60 = 120°

We know that,

$\boxed{\sf The \: opposite \: angles \: of \: parallelogram \: are \: equal \: and \: parallel }$

• Opposite side of 60° is 60°
• Opposite side of 120° is 120°

Hence, the measures of all angles of the parallelogram is 60°, 120°, 60°, 120°.

$\underline{\bf Verification :}$

We know that,

$\boxed{\sf The \: sum \: of \: all \: four \: angles \: of \: a \: parallelogram \: is \: 360\degree}$

$\implies$60 + 120 + 60 + 120 = 360

$\implies$360 = 360

HENCE VERIFIED