Question

help me guys in this problem​

Answer 1

To find:-

• Value of x and y

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$\large \tt \: ☃ Step \: by \: step \: explanation$

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(i)

We know that,

Sum of any two interior angles of triangle is equal to one exterior angle.

So,

⇒30° + x = 94°

⇒x = 94°- 30

⇒x = 64°

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Verification:-

⇒30° + x = 94°

• Put x = 64°

⇒30° + 64° = 94°

⇒94° = 94°

Hence, verified.⠀⠀⠀⠀⠀⠀⠀

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(ii)

The given triangle is Right angle triangle. So, it's one angle is of 90°.

We know that,

Sum of all interior angles of triangle is 180°

So,

⇒3y + 2y + 90° = 180°

⇒5y = 180° - 90°

⇒5y = 90°

⇒y = 90°/5

⇒y = 18°

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2y = 2 × 18° = 36°

3y = 3 × 18° = 54°

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Verification:-

⇒3y + 2y + 90° = 180°

• Put 3y = 54° and 2y = 36°

⇒54° + 36° + 90° = 180°

⇒90° + 90° = 180°

⇒180° = 180°

Hence, verified.

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Therefore, x = 64° and y = 18°

Answer 2

Question :-

To Find the value of x and y in the following above figures .

Solution (i):-

To Find :-

The value of :-

• x

Given :-

• $\bf{\angle CAB = 30^{\circ}}$

• $\bf{\angle D = 94^{\circ}}$

• $\bf{\angle ACB = x}$

We know :-

• The opposite angles of a triangle are equal.

• The angle on a straight line is 180°.

• The sum of all the angles sum up to 180°.

Concept :-

First we have to find the $\angle$CBA.

We Know that the angle on a straight line is equal to 180° , and the given angle is 94° , so the sum of angle angle D and angle B will be 180° , so the equation formed is :-

$\boxed{\bf{\angle_{D} + \angle_{B} = 180^{\circ}}}$

So putting the value of angle D in the Equation ,we get :-

A/c :-

$:\implies \bf{\angle_{D} + \angle_{B} = 180^{\circ}} \\ \\ \\ :\implies \bf{94^{\circ} + \angle_{B} = 180^{\circ}} \\ \\ \\ :\implies \bf{\angle_{B} = 180^{\circ} - 94^{\circ}} \\ \\ \\ :\implies \bf{\angle_{B} = 86^{\circ}} \\ \\ \\ \therefore \purple{\bf{\angle_{B} = 86^{\circ}}}$

Hence, the angle B is 86°.

Calculation :-

To Find the value of x :-

Given :-

• $\bf{\angle CAB = 30^{\circ}}$

• $\bf{\angle CBA = 86^{\circ}}$

Using the Property of a triangle that all the three angles of a triangle sum up to 180° , we get :-

$:\implies \bf{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}} \\ \\ \\ :\implies \bf{\angle_{ACB} + \angle_{CAB} + \angle_{CBA} = 180^{\circ}} \\ \\ \\ :\implies \bf{x + 30^{\circ} + 86^{\circ} = 180^{\circ}} \\ \\ \\ :\implies \bf{x + 116^{\circ} = 180^{\circ}} \\ \\ \\ :\implies \bf{x = 180^{\circ} - 116^{\circ}} \\ \\ \\ \bf{x = 64^{\circ}} \\ \\ \\ \therefore \purple{\bf{x = 64^{\circ}}}$

Hence, the value of x is 64°.

Solution (ii) :-

To Find :-

The value of :-

• y

Given :-

• $\bf{\angle CAB = 90^{\circ}}$

• $\bf{\angle D = 94^{\circ}}$

• $\bf{\angle ACB = 3y}$

• $\bf{\angle ABC = 2y}$

We Know :-

• The sum of all the angles sum up to 180°.

• If a Triangle is a right-angled then the sum of opposite Sides will be Equal to 90°.

Calculation :-

Method (i) :-

Using the Property of a triangle that all the three angles of a triangle sum up to 180° , we get :-

$:\implies \bf{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}} \\ \\ \\ :\implies \bf{\angle_{ACB} + \angle_{CAB} + \angle_{CBA} = 180^{\circ}} \\ \\ \\ :\implies \bf{3y + 90^{\circ} + 2y = 180^{\circ}} \\ \\ \\ :\implies \bf{5y + 90^{\circ} = 180^{\circ}} \\ \\ \\ :\implies \bf{5y = 180^{\circ} - 90^{\circ}} \\ \\ \\ :\implies \bf{5y = 90^{\circ}} \\ \\ \\ :\implies \bf{y = \dfrac{90^{\circ}}{5}} \\ \\ \\ :\implies \bf{y = 18^{\circ}} \\ \\ \\ \therefore \purple{\bf{y = 18^{\circ}}}$

Hence, the value of y is 18°.

Method (ii) :-

Using the Property of a triangle that If a Triangle is a right-angled then the sum of opposite Sides will be Equal to 90° , we get :-

$:\implies \bf{\angle ACB + \angle ABC = 90^{\circ}} \\ \\ \\ :\implies \bf{3y + 2y = 90^{\circ}} \\ \\ \\ :\implies \bf{5y = 90^{\circ}} \\ \\ \\ :\implies \bf{y = \dfrac{90^{\circ}}{5}} \\ \\ \\ :\implies \bf{y = 18^{\circ}} \\ \\ \\ \therefore \purple{\bf{y = 18^{\circ}}}$

Hence, the value of y is 18°.