Question

Two angles of a quadrilateral are 56 0 and 1120.If the other two angles are equal,
find the equal angles.

Answer 1

Angles in a quadrilateral = 360 degrees

56+112+x+x = 360

= 168 +2x= 360

= 2x= 360-168

= 2x = 192

x = 96

The equal angles are 96 degrees

Answer 2

Given :

• Two angles of a quadrilateral are 560 and 1120.
• Other two angles are equal.

To Find :

• The equal angles.

Calculations :

❖ Here we are provided with two angles of a quadrilateral which are 560° & 1120°. And also the other two angles are equal. So let's assume the other two angles which are equal as 'x' which can be written as $\boxed{ \rm{ \green{x + x}}}$ since two angles are equal. Now, as we know that Sum of all angles of a quadrilateral are 360°. So we'll add all the angles and will calculate the equal angles.

We know that,

• $\boxed{ \rm{ \pmb{ \pink{ \underline{Sum \: of \: all \: angles_{(Quadrilateral)} = 360^{\circ}}}}}}$

Firstly let's calculate the angles [560° and 1120°] in simplest form.

• For this, we need to cancel the zeroes.

On cancelling,

• 56° and 112° are the two angles of a quadrilateral.

Now, let's put the values and add up the angles,

$\longrightarrow \sf x + x + 56^{\circ} + 112^{\circ} = 360^{\circ}$

• By adding x + x, we will write x + x as 2x.

On adding all the numbers,

$\longrightarrow \sf 2x + 168^{\circ} = 360^{\circ}$

Now changing the sign from (+) to (-) and performing subtraction [360 - 168]

$\longrightarrow \sf 2x = 360^{\circ} - 168^{\circ}$

On subtracting the numbers,

$\longrightarrow \sf 2x = 192^{\circ}$

Now, transposing 2 to R.H.S on the denominator of angle 192°, and performing division,

$\longrightarrow \sf x = \cancel\dfrac{192}{2}$

By cancelling the numbers,

$\longrightarrow \sf \boxed{ \rm{ \pmb{ \red{x = 96^{\circ}}}}}$

Therefore,

• The measure of each of these angle [of two equal angles] is 96°.

$\dag$ Verification :

Now let's check that the angles are adding up to 360° or not.

The angles are :-

• 112°
• 56°
• 96°
• 96°

And as we know that,

• Sum of all angles of a quadrilateral = 360°

→ 112° + 56° + 96° + 96° = 360°

→ 168° + 192° = 360°

→ 360° = 360°

Hence, verified!