Question

On no. 13
Find the angles of a triangle which are in the ratio 4:3:2.

Answer 1

Answer:

80°, 60° & 40°

Step-by-step explanation:

Let 4x ,3x & 2x be the angles of the ∆.

According to question,

4x + 3x + 2x = 180°

Finding x :

4x + 3x + 2x = 180°

⇒4x + 5x = 180°

⇒9x = 180°

⇒x = 180°/9

⇒x = 20°

$\rm\blue{.°. x=20°}$

Finding angles :

• 4x = 4 × 20° = 80°
• 3x = 3 × 20° = 60°
• 2x = 2 × 20° = 40°

Hence, the three angles are 80°, 60° & 40°.

Why&How 4x + 3x + 2x = 180°?

As the given figure is a triangle, so we know that all the angles sum is 180°. It is called the angle sum property of triangle.

Hence, 4x + 3x + 2x = 180°.

Answer 2

Step-by-step explanation:

Given:-

In a triangle the angles are in ratio of 4:3:2

To find:-

Measure of each angle

Solution:-

Let the angles be 4x,3x,2x

• According to angle sum property in a triangle

$\boxed{\sf Sum\:of\:Angles=180°}$

• Substitute the values

$\\\qquad\quad\sf {:}\longrightarrow 4x+3x+2x=180$

$\\\qquad\quad\sf {:}\longrightarrow 7x+2x=180$

$\\\qquad\quad\sf {:}\longrightarrow 9x=180$

$\\\qquad\quad\sf {:}\longrightarrow x=\dfrac {180}{9}$

$\\\qquad\quad\sf {:}\longrightarrow x=20$

$\rule {200}{1}$

$\\\qquad\quad\sf {:}\longrightarrow 4x=4\times 20=80°$

$\\\qquad\quad\sf {:}\longrightarrow 3x=3\times 20=60°$

$\\\qquad\quad\sf {:}\longrightarrow 2x=2\times 20=40°$

$\\\\\therefore\sf The\:angles\:are\:80°,60°,40°.$

Explore more:-

Formulas of Areas to remember:-

$\\ \star\sf Square=(side)^2 \\ \star\sf Rectangle=Length\times Breadth \\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2$