Question

three angles of a quadrilateral are 65⁰,100⁰,85⁰.find the measure of fourth angle. with working please ​

Answer 1

$\underline{ \underline{ \Large \bf { Answer:} } }$

110°

$\underline{ \underline{ \Large \bf { Given:} } }$

• Three angles of a quadrilateral are 65° , 100° , 85°.

$\underline{ \underline{ \Large \bf { To \: calculate:} } }$

• The measure of fourth angle.

$\underline{ \underline{ \Large \bf { Clarification:} } }$

Here, we are provided with the measure of 3 angles of the quadrilateral. We have to find out the measure of the fourth angles. So, basically we have to apply here the angle sum property of the quadrilateral.

Angle sum property of a quadrilateral :

• Angle sum property of a quadrilateral states that the sum of all angles of a quadrilateral is equivalent to 360°.

By forming a linear equation, we'll find the measure of the fourth angle.

$\underline{ \underline{ \Large \bf { Calculation:} } }$

Let the fourth angle be "x°".

As we know that,

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

According to the question,

$\implies$ First angle + Second angle + Third angle + Fourth angle = 360°

$\implies$ 65° + 100° + 85° + x° = 360°

• Performing addition.

$\implies$ 250° + x° = 360°

• Transposing 250° from LHS to RHS.

$\implies$ x° = 360° - 250°

$\implies$ x° = 110°

$\implies \pmb {\rm \red{Fourth \: angle = {110}^{\circ} } }$

Therefore, fourth angle of the quadrilateral is 110°.

$\underline{ \underline{ \Large \bf { Verification:} } }$

As we know that,

★ $\boxed {\sf {Sum \: of \: angles \: of \: quadrilateral = {360}^{\circ} } }$

LHS:

$\implies$ 65° + 100° + 85° + x°

$\implies$ 65° + 100° + 85° + 110°

$\implies$ 360°

RHS:

$\implies$ 360°

LHS = RHS

Henceforth, verified!!

Answer 2

Sum of interior angles of a □ = 360°

Let the fourth angle be of = x°

∴ 65° + 100° + 85° + x° = 360°

⇒ x° + 250° = 360°

⇒ x° = 360° - 250° = 110°.

∴ The unknown angle measures 110°.