Question

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Answer 1

Question 5 :

Answer :

The measure of two angles are :-

• The one angle = 80°.
• The other angle = 100°.

Given :

• One angle of the supplementary angle = $\sf \dfrac{4}{5}$

To Find :

• The measure of other angle of the supplementary angle.

Solution :

Let,

The one angle be $\sf\bigg(\dfrac{4}{5}\bigg)x$

The other angle be x.

According to the question,

Sum of two angles are supplementary.

We know that,

Sum of two supplementary angles is 180°

That means,

$\bf \implies \bigg(\dfrac{4}{5}\bigg)x + x = 180 ^{ \circ} \\ \\ \\ \bf \implies \dfrac{4x \times 1 + x \times 5}{5} = {180}^{ \circ} \\ \\ \\ \bf \implies \dfrac{4x + 5x}{5} = {180}^{ \circ} \\ \\ \\ \bf \implies 9x = {180}^{ \circ} \times 5 \\ \\ \\ \bf \implies 9x = {900}^{ \circ} \\ \\ \\ \bf \implies x = \frac{ {900}^{ \circ} }{9} \\ \\ \\ \bf \implies x = {100}^{ \circ} \\ \\ \\ \: \: \bf\therefore \: \: x = {100}^{ \circ}$

So, the measure of two angles are :-

★ The one angle = $\sf{\bigg(\dfrac{4}{5}\bigg)x = \dfrac{4}{5} \times 100 = \dfrac{400}{5} = {80}^{\circ}}$

★ The other angle = x = 100°

Hence,

The measures of two angles are 80° and 100°.

______________________________

Question 6 :

Answer :

The measure of two angles of the linear pair :-

• The first angle = 120°.
• The second angle = 60°.

Given :

• The ratio of two angles of a linear pair = 2 : 1.

To Find :

• The measure of the angles.

Solution :

Let,

The first angle of the linear pair be 2x.

The second angle of the linear pair be 1x OR x.

We know that,

Linear pair = 180°

That means,

First angle + Second angle = 180°

$\bf \implies 2x + x = {180}^{ \circ} \\ \\ \\ \bf \implies 3x = {180}^{ \circ} \\ \\ \\ \bf \implies x = \frac{ {180}^{ \circ} }{3} \\ \\ \\ \bf \implies x = {60}^{ \circ} \\ \\ \\ \: \: \bf \therefore \: \: x = {60}^{ \circ}$

So, the measure of two angles of the linear pair are :

★ The first angle = 2x = 2 × 60° = 120°

★ The second angle = 1x = 1 × 60° = 60°

Hence,

The measure of two angles of the linear pair are 120° and 60°.

______________________________

Question 7 :

Answer :

The measure of two adjacent angles are :-

• The one angle = 48°.
• The other angle = 28°.

Given :

• The sum of two adjacent angle = 76.
• The one of them measure 20 more than the other.

To Find :

• The measure of the other adjacent angle.

Solution :

Let,

The other angle of the adjacent angle be x.

The one angle of the adjacent angle be x + 20°.

According to the question,

The sum of two adjacent angles is 76.

That means,

$\bf \implies x + x + {20}^{ \circ} = {76}^{ \circ} \\ \\ \\ \bf \implies 2x + {20}^{ \circ} = {76}^{ \circ} \\ \\ \\ \bf \implies 2x = {76}^{ \circ} - {20}^{ \circ} \\ \\ \\ \bf \implies 2x = {56}^{ \circ} \\ \\ \\ \bf \implies x = \frac{ {56}^{ \circ} }{2} \\ \\ \\ \bf \implies x = {28}^{ \circ} \\ \\ \\ \: \: \bf \therefore \: \: x = {28}^{ \circ}$

So, the measure of two angles are :

★ The other angle of the adjacent angle = x = 28°.

★ One angle of the adjacent angle = x + 20° = 28° + 20° = 48°

Hence,

The measure of two adjacent angles are 28° and 48°.

Answer 2

Step-by-step explanation:

Question 5 :

Answer :

The measure of two angles are :-

The one angle = 80°.

The other angle = 100°.

Given :

One angle of the supplementary angle = \sf \dfrac{4}{5}54

To Find :

The measure of other angle of the supplementary angle.

Solution :

Let,

The one angle be \sf\bigg(\dfrac{4}{5}\bigg)x(54)x

The other angle be x.

According to the question,

Sum of two angles are supplementary.

We know that,

Sum of two supplementary angles is 180°

That means,

\begin{gathered} \bf \implies \bigg(\dfrac{4}{5}\bigg)x + x = 180 ^{ \circ} \\ \\ \\ \bf \implies \dfrac{4x \times 1 + x \times 5}{5} = {180}^{ \circ} \\ \\ \\ \bf \implies \dfrac{4x + 5x}{5} = {180}^{ \circ} \\ \\ \\ \bf \implies 9x = {180}^{ \circ} \times 5 \\ \\ \\ \bf \implies 9x = {900}^{ \circ} \\ \\ \\ \bf \implies x = \frac{ {900}^{ \circ} }{9} \\ \\ \\ \bf \implies x = {100}^{ \circ} \\ \\ \\ \: \: \bf\therefore \: \: x = {100}^{ \circ} \end{gathered}⟹(54)x+x=180∘⟹54x×1+x×5=180∘⟹54x+5x=180∘⟹9x=180∘×5⟹9x=900∘⟹x=9900∘⟹x=100∘∴x=100∘

So, the measure of two angles are :-

★ The one angle = \sf{\bigg(\dfrac{4}{5}\bigg)x = \dfrac{4}{5} \times 100 = \dfrac{400}{5} = {80}^{\circ}}(54)x=54×100=5400=80∘

★ The other angle = x = 100°

Hence,

The measures of two angles are 80° and 100°.

______________________________

Question 6 :

Answer :

The measure of two angles of the linear pair :-

The first angle = 120°.

The second angle = 60°.

Given :

The ratio of two angles of a linear pair = 2 : 1.

To Find :

The measure of the angles.

Solution :

Let,

The first angle of the linear pair be 2x.

The second angle of the linear pair be 1x OR x.

We know that,

Linear pair = 180°

That means,

First angle + Second angle = 180°

\begin{gathered}\bf \implies 2x + x = {180}^{ \circ} \\ \\ \\ \bf \implies 3x = {180}^{ \circ} \\ \\ \\ \bf \implies x = \frac{ {180}^{ \circ} }{3} \\ \\ \\ \bf \implies x = {60}^{ \circ} \\ \\ \\ \: \: \bf \therefore \: \: x = {60}^{ \circ} \end{gathered}⟹2x+x=180∘⟹3x=180∘⟹x=3180∘⟹x=60∘∴x=60∘

So, the measure of two angles of the linear pair are :

★ The first angle = 2x = 2 × 60° = 120°

★ The second angle = 1x = 1 × 60° = 60°

Hence,

The measure of two angles of the linear pair are 120° and 60°.

______________________________

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