Question

angle of a trangle are In the ratio 4:3:2. find the measure of each angle.​

Answer 1

Let the measures of the given angles of the triangles be (4x)°, (3x)° and (2x)° respectively.

Then, = 4x + 3x + 2x = 180° --- [∵sum of the angles of a triangle is 180°]

= 9x = 180°

= x = 180/9

= x = 20

So, the angle measures (4 × 20)°o, (3 × 20)°, (2 × 20)°,

i.e., 80°, 60°, 40°.

Hence, the angles of the triangles are 80°, 60°, 40°.

Answer 2

Concept used

Angle sum property (triangle) :- This property is only applicable for triangles. It might be any triangle, equilateral, isosceles or scalene. This property is also applicable for all the types of angle based triangles. All the figures that has three sides and angles should have the sum of their angles as 180°. This is the rule of this concept. If this rule is not accepted by any triangle, then that figure cannot be classified as a triangle. This same rule will be used in this question.

$\sf \dashrightarrow {Angle \: sum \: property}_{(Triangle)} = {180}^{\circ}$

${\sf \dashrightarrow 4 : 3 : 2 = {180}^{\circ}}$

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

${\sf \dashrightarrow 9x = {180}^{\circ}}$

${\sf \dashrightarrow x = \dfrac{180}{9}}$

${\sf \dashrightarrow x = 20}$

Now, we can find the measurements of each angle.

Measurement of first angle :

${\sf \dashrightarrow 4x = 4(20)}$

${\sf \dashrightarrow {80}^{\circ}}$

Measurement of second angle :

${\sf \dashrightarrow 3x = 3(20)}$

${\sf \dashrightarrow {60}^{\circ}}$

Measurement of third angle :

${\sf \dashrightarrow 2x = 2(20)}$

${\sf \dashrightarrow {40}^{\circ}}$

Hence, the angles of the triangle are 80°, 60° and 40° respectively.