Question

The measure of two angles of quadrilateral are 120 degrees and 40 degrees and the other two angles are equal. Find the measure of the equal angles.

Answer 1

Given :

• Measure of $\sf{angle}_{1}$= 120°

• Measure of $\sf{angle}_{2}$ = 40°

• Other two angles are equal

To Find :

• Measure of the equal angles

Solution :

Let the other angle be x as they are equal both of 'em will be assumed as x

We know that :

$\bigstar \: \: \boxed{ \sf \: Sum \: of \: all \: angles \: of \: Quadrilateral = {360}^{ \circ} }$

$\longrightarrow \sf \: x + x + {120}^{ \circ}+{40}^{\circ} = 360$

$\longrightarrow \sf \: 2x + {120}^{ \circ}+ {40}^{ \circ}= {360}^{\circ}$

$\longrightarrow \sf \: 2x +{160}^{ \circ}= 360^{\circ}$

$\longrightarrow \sf \: 2x = {360}^{ \circ} - {160 }^{ \circ}$

$\longrightarrow \sf \: 2x = {200}^{ \circ}$

$\longrightarrow \sf \: x = \cancel\dfrac{200}{2}$

$\longrightarrow \sf \red{ x = {100}^{ \circ} }$

$\therefore$ Measure of each equal angle = 100°

Verification :

$\bigstar \: \: \boxed{ \sf \: Sum \: of \: all \: angles \: of \: Quadrilateral = {360}^{ \circ} }$

$\longrightarrow \sf \: {100}^{ \circ}+ {100}^{ \circ} + {120}^{ \circ} + {40}^{ \circ}={360}^{ \circ}$

$\longrightarrow \sf \: {200}^{ \circ}+ {160}^{ \circ} = {360}^{ \circ}$

$\longrightarrow \sf \: {360}^{ \circ}= {360}^{ \circ}$

Hence, Verified!

Answer 2

Answer:

• Angle₁ = 120°
• Angle₂ = 40°
• Angle₃ and Angle₄ are Equal.

Let the Angle₃ and Angle₄ be n.

• According to the Question :

⇴ Sum of Angles of Quadrilateral = 360°

⇴ 120° + 40° + n + n = 360°

⇴ 160° + 2n = 360°

⇴ 2n = 360° – 160°

⇴ 2n = 200

• Dividing both term by 2

⇴ n = 100° = (Angle₃ & Angle₄)

∴ Equal Angles of Quadrilateral are 100°.

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• VERIFICATION :

⇢ Sum of Angles of Quadrilateral = 360°

⇢ 120° + 40° + n + n = 360°

⇢ 160° + 100° + 100° = 360°

⇢ 360° = 360°⠀ Hence, Verified!