Question

In the adjoining figure, find the value of x

Please Answer I Will Mark You As BRAINLIEST​​

Answer 1

Given :

• ∠POR = (3x + 20)°
• ∠ROQ = (4x - 36)°

To Find :

The value of x.

Solution :

Analysis :

Here we know that all angles in a straight line sum upto 180°. We can use this information to find the x by forming a equation and equating it.

Explanation :

We know that all angles in a straight line sum upto 180°.

☯ According to the question,

⇒ ∠POR + ∠ROQ = 180°

⇒ (3x + 20)° + (4x - 36)° = 180°

⇒ 3x + 20 + 4x - 36 = 180°

⇒ 3x + 4x + 20 - 36 = 180°

⇒ 7x - 16 = 180°

⇒ 7x = 180 + 16

⇒ 7x = 196

⇒ x = 196/7

⇒ x = 28

∴ x = 28.

The angles :

• ∠POR = (3x + 20)° = (3 × 28 + 20)° = (84 + 20)° = 104°
• ∠ROQ = (4x - 36)° = (4 × 28 - 36)° = (112 - 36)° = 76°

The value of the x is 28.

Verification :

LHS :

⇒ ∠POR + ∠ROQ

⇒ 104° + 76°

⇒ 180°

∴ LHS = 180°.

∴ RHS = 180°.

∴ LHS = RHS.

• Hence verified.

Explore More :

• Angles which are more than 0° but less than 90° are called Acute Angles.
• Angles which are more than 90° but less than 180° are called Obtuse Angles.
• Angles which are exactly 90° are called Right angles.
• Angles which are exactly 180° are called Straight angles.
• Angles which are more than 180° but less than 360° are called Reflex Angles.
• Angles which are exactly 360° are called Complete angles.

Answer 2

Step-by-step explanation:

Given:

• ∠POR = (3x + 20)°.
• ∠ROQ = (4x - 36)°.

Need to find: Value of x ?

❏ Here we are asked to find out the value of x. Through the given adjoining figure we know that all the angles sum upto 180°. So by using this data we will find the value of x.

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__________________

‎

$\frak{\underline{\underline{\dag As\ we\ know\ that\ :-}}}$

‎

$\star\;\boxed{\sf{\pink{Sum\ of\ all\ angles\ in_{(straight\ line)}\ =\ 180^{\circ}.}}}$

‎

$\bf {Here} \begin{cases} &\sf{\angle POR\ =\ (3x\ +\ 80)^{\circ}.} \\ &\sf{\angle ROQ\ =\ (4x\ -\ 36)^{\circ}.} \end{cases}$

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$\boldsymbol{\underline{\bigstar According\ to\ the\ question\ :-}}$

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$\sf : \implies {\angle POR\ +\ \angle ROQ\ =\ 180^{\circ}} \\ \\ \\ \sf : \implies {(3x\ +\ 20)^{\circ}\ +\ (4x\ -\ 36)^{\circ}\ =\ 180^{\circ}} \\ \\ \\ \sf : \implies {3x\ +\ 20\ +\ 4x\ -\ 36\ =\ 180^{\circ}} \\ \\ \\ \sf : \implies {3x\ +\ 4x\ +\ 20\ -\ 36\ =\ 180^{\circ}} \\ \\ \\ \sf : \implies {7x\ -\ 16\ =\ 180^{\circ}} \\ \\ \\ \sf : \implies {7x\ =\ 180\ +\ 16} \\ \\ \\ \sf : \implies {7x\ =\ 196} \\ \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{196}{7}} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf x\ =\ 28.}}}}\bigstar$

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Therefore,

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• ∠POR = (3x + 20)° = (3 × 28 + 20)° = (84 + 20)° = 104°.

• ∠ROQ = (4x - 36)° = (4 × 28 - 36)° = (112 - 36)° = 76°.

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$\sf \therefore {\underline{Hence,\ the\ value\ of\ x\ is\ \bf 28.}}$

‎

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar Verification \bigstar}}}}}\mid}\\\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\sf : \implies {\angle POR\ +\ \angle ROQ\ =\ 180^{\circ}}$

$\sf : \implies {104^{\circ}\ +\ 76^{\circ}\ =\ 180^{\circ}}$

$\sf : \implies {180^{\circ}\ =\ 180^{\circ}}$

$\sf : \implies {\underline{\boxed{\purple{\bf L.H.S\ =\ R.H.S}}}}\bigstar$

‎

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar More\ to\ know \bigstar}}}}}\mid}\\\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

❏ Properties of supplementary angle:-

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• The two angles are said to be supplementary angles when they add up to 180°.

• The two angles together make a straight line, but the angles need not be together.

• “S” of supplementary angles stands for the “Straight” line. This means they form 180°.