Question

the angles of a triangle are in the ratio 4:3:2, determine the three angles​

Answer 1

Answer:

Given :-

• The angles of a triangle are in the ratio of 4 : 3 : 2.

To Find :-

• What are the angles of a triangle.

Solution :-

Let,

$\leadsto \bf First\: Angle_{(Triangle)} =\: 4x$

$\leadsto \bf Second\: Angle_{(Triangle)} =\: 3x$

$\leadsto \bf Third\: Angle_{(Triangle)} =\: 2x$

As we know that :

$\footnotesize\bigstar\: \sf\boxed{\bold{\pink{Sum\: of\: the\: angles\: of\: a\: triangle =\: 180^{\circ}}}}\: \: \bigstar\:$

According to the question by using the formula we get,

$\implies \sf 4x + 3x + 2x =\: 180^{\circ}$

$\implies \sf 7x + 2x =\: 180^{\circ}$

$\implies \sf 9x =\: 180^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{9}}$

$\implies \sf\bold{\purple{x =\: 20^{\circ}}}$

Hence, the required angles of a triangle are :

✫ First Angle Of Triangle :-

➸ First Angle = 4x

➸ First Angle = 4(20°)

➸ First Angle = 80°

✫ Second Angle Of Triangle :-

➸ Second Angle = 3x

➸ Second Angle = 3(20°)

➸ Second Angle = 60°

✫ Third Angle Of Triangle :-

➸ Third Angle = 2x

➸ Third Angle = 2(20°)

➸ Third Angle = 40°

$\therefore$ The angles of a triangle are 80°, 60° and 40° respectively.

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Answer 2

$\bull$ Given :-

• The angles of a triangle are in ratio 4 : 3 : 2

$\bull$ To Determine :-

• The value of the respective angles

$\bull$ϲοиϲєρτ :-

: In this question we will use the concept of "angle sum property of a Triangle". This property or theorem states that the sum of the measures of a triangle is always 180°. We will let the values of each angle and just sum them up and take R.H.S. as 180° and further equate it.

$\bull$ Solution :-

: Let the value of angles be :-

• angle 1 = 4x
• Angle 2 = 3x
• Angle 3 = 2x

Now, using the angle sum property of a Triangle, we know that, the sum of these angles is 180°, therefore,

$\sf : \implies \: 4x + 3x + 2x =180^\circ \\ \sf : \implies \:9x = 180 ^\circ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies \:x = \frac{180}{9} = 20 ^\circ \: \: \: \: \: \: \: \: \: \: \:$

Since the value of x is "20°", therefore,

• angle 1 = 4x = 4 x 20° = 80°
• Angle 2 = 3x = 3 x 20° = 60°
• Angle 3 = 2x = 2 x 20° = 40°

$\bull$ νєяiƒiϲατiοи :-

To verify we will just add the values of all the angles and check whether the value is equal to 180° or not. If L.H.S. will be equal to R.H.S., therefore, the values will be verified. So let's do it.

$\sf : \implies \: 80 + 40 + 60 = 180 \\ \sf : \implies \: 180^\circ = 180 ^\circ\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf : \implies \:L.H.S. = R.H.S \: \: \: \: \: \: \: \:$

Now, since L.H.S. is equal to R.H.S., hence verified.