Question

In a quadrilateral two angles are 80", 120º and the remaining two angles are equal. What is the measure of each angle?​

Answer 1

Step-by-step explanation:

Given :-

In a quadrilateral two angles are 80°, 120º and the remaining two angles are equal.

To find :-

What is the measure of each angle?

Solution :-

Given that

The two angles of a Quadrilateral = 80° and 120°

The remaining angles are equal.

Let the other two angles be X° and X°

We know that

The sum of all four interior angles in a Quadrilateral is 360°

=> 80°+120°+X°+X° = 360°

=> 200°+2X° = 360°

=> 2X° = 360°-200°

=> 2X° = 160°

=> X° = 160°/2

=> X° = 80°

Therefore, X = 80°

The remaining angles on the given quadrilateral are 80° and 80°

Answer:-

The measure of remaining each angle is 80°

Used formulae:-

→ The sum of all four interior angles in a Quadrilateral is 360°

Answer 2

Answer:

Given :-

• In a quadrilateral two angles are 80° and 120° and the remaining two angles are equal.

To Find :-

• What is the measure of each angles of a quadrilateral.

Solution :-

Let,

$\mapsto$ The measure of each remaining angles of a quadrilateral be x

As we know that :

$\small \bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: angles_{(Quadrilateral)} =\: 360^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 80^{\circ} + 120^{\circ} + x + x =\: 360^{\circ}$

$\implies \sf 200^{\circ} + 2x =\: 360^{\circ}$

$\implies \sf 2x =\: 360^{\circ} - 200^{\circ}$

$\implies \sf 2x =\: 160^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{160^{\circ}}}{\cancel{2}}$

$\implies \sf x =\: \dfrac{80^{\circ}}{1}$

$\implies \sf\bold{\red{x =\: 80^{\circ}}}$

$\therefore$ The measure of the two remaining angles of a quadrilateral is 80° each .

VERIFICATION :-

$\leadsto \sf 80^{\circ} + 120^{\circ} + x + x =\: 360^{\circ}$

By putting x = 80° we get,

$\leadsto \sf 80^{\circ} + 120^{\circ} + 80^{\circ} + 80^{\circ} =\: 360^{\circ}$

$\leadsto \sf\bold{\purple{360^{\circ} =\: 360^{\circ}}}$

$\dashrightarrow \bf L.H.S =\: R.H.S$

HENCE VERIFIED .