Question

Three angles of a quadrilateral measures 36⁰,72⁰ and 114⁰. Find the measure of 4th angle

pls explain​

Answer 1

Answer:

The fourth angle of the quadrilateral is 138°

Step-by-step explanation:

We Have :-

The angles of a quadrilateral

Angle 1 = 36°

Angle 2 = 72°

Angle 3 = 114°

To Find :-

Measure of the 4th angle

Property Used :-

The sum of all the angles of a quadrilateral is 360°

Solution :-

$sum \: of \: all \: the \: angles \: of \: a \: quadrilateral \: = \: 360 \\ \\ 36 + 72 + 114 + x = 360 \\ \\ 222 + x = 360 \\ \\ x = 360 - 222 \\ \\ x = 138 \\ \\ the \: fourth \: angle \: of \: the \: quadrilateral \: is \: 138$

Answer 2

Answer:

Given

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Three angles of a quadrilateral

• ↝ 36⁰
• ↝ 72⁰
• ↝ 114⁰

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To Find

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• ↝ Measurement of 4th angle.

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Solution

There are given 3 angles measurement.

Let the fourt angle be X⁰.

And we know that the measurement of of a quadrilateral is 360⁰

So,

$: \implies\sf \pink{36\degree+ 72 \degree + 114 \degree +x \degree }= \bf\purple{360 \degree} \\ \\ : \implies \sf \pink{222 \degree + x \degree} = \bf\purple{360 \degree} \\ \\ \: \: \: \: \: : \implies \sf \pink{x} = \bf \purple{360 \degree - 222 \degree} \\ \\ : \implies\sf \pink{x \degree} = \bf \purple{138\degree} \\ \\ \Large\underline{\boxed{\sf \purple{ \: \: x \degree} =\bf \pink{138\degree}}}$

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Verification

As we know that that the measurement of of a quadrilateral is 360⁰.

So,

$: \implies\sf \pink{36\degree+ 72 \degree + 114 \degree +x \degree }= \bf\purple{360 \degree} \\ \\ \star\bf\underline{Putting \: value \: of \: x } \star\\ \\ \: \: \: \: \: : \implies\sf \pink{36\degree+ 72 \degree + 114 \degree +138\degree }= \bf\purple{360 \degree} \\ \\ : \implies \bf \pink{360\degree } = \bf\purple{360 \degree} \\ \\ \Large\underline{\boxed{\bf \purple{ \: \: 360 \degree} =\bf \pink{360\degree}}} \\ \sf \underline {Hence \: Verified}$

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Therefore

• ➠ The measurement of 4th angle is 138⁰.