Question

4) If one angle of a parallelogram is 40°, what are the measures of the other angles?

Plz and step by step and don't ans do it on your own and all that plz
need it fast​

Answer 1

✬ Angles = 140° , 140° ✬

Step-by-step explanation:

Given:

• Measure of one angle of parallelogram is of 40°.

To Find:

• What are the measures of other angles?

Solution: Let ABCD be a || gm and measure of other two angles be x°.

[ A Parallelogram is type of quadrilateral in which opposite sides are parallel and opposite angles are equal to each other ]

Therefore,

• ∠A = ∠C = 40°
• ∠B = ∠D = x°

As we know that

★ Sum of all angles of ||gm = 360° ★

$\implies{\rm }$ ∠A + ∠B + ∠C + ∠D = 360°

$\implies{\rm }$ 40° + x + 40° + x = 360°

$\implies{\rm }$ 80° + 2x = 360°

$\implies{\rm }$ 2x = 360° – 80°

$\implies{\rm }$ 2x = 280°

$\implies{\rm }$ x = 280°/2°

$\implies{\rm }$ x = 140

Hence,

➬ ∠A = ∠C = 40° and

➬ ∠B = ∠D = 140°

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{angles \: of \: parrellelogram \: are \angle{Q} \: - {110}^{0} \: \angle{R} - {7 0 }^{0} \: and \: \angle{S} - {110}^{0} }}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}}$

$\tt : \implies one \: angle \: of \: a \: parallelogram \: is \: {40}^{0}$

$\red{\underline \bold{To \: Find :}}$

$\tt : \implies what \: are \: the \: measures \: of \: the \: other \: angles?$

• Given Question

$\tt : \implies \: let \: the \: parrellelogram \: be \: PQRS$

$\tt : \implies \angle{P} - 7 0(given)$

$\tt : \implies \angle{R} - 70(opposites \: angle \: of \: parrllelogram \: are \: equal$

$\tt : \implies \angle{P} + \angle{Q} = 180$

$\tt : \implies\angle{P} = 70$

$\tt : \implies\angle{Q} + 70 - 180$

$\tt : \implies\angle{Q} = 180 - 70$

$\tt : \implies\angle{Q} = 110$

$\tt : \implies \angle{Q} = \angle{S}$

$\tt : \implies \angle{Q} \: and \: are \: equal \: \angle{S}$

$\tt : \implies\angle{S} = 110$

$\green{\tt{\therefore{angles \: of \: parrellelogram \: are \angle{Q} \: - {110}^{0} \: \angle{R} - {7 0 }^{0} \: and \: \angle{S} - {110}^{0} }}}$