Question

the angles of the triangle are in the ratio of 1:3:5. Find the measure of each one of the angles
​

Answer 1

Given :-

• The angles of the triangle are in the ratio of 1 : 3 : 5

To Find :-

• Measure of each angle of that triangle

Solution :-

~Here , we're given the ratio of the angles of triangle and we need to find the measure of each one of them by using the angle sum property of the triangle which means that sum of all angles of any triangle is always 180°.

According to the given ratios ::

Angles will be

• x
• 3x
• 5x

Finding the measure of each angle :-

$\sf \leadsto x + 3x + 5x = 180$

$\sf \leadsto 9x = 180$

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

$\;\;\;\;\qquad\quad\quad\quad\boxed{\sf{x=20}}$

Therefore :-

${\underline{\bf{ \star \;\;\;x=20}}}$

${\underline{\bf{ \star \;\;\;3x=60}}}$

${\underline{\bf{ \star \;\;\;5x=100}}}$

→ Measures of the angles of triangle are 20° , 60° and 100°

Answer 2

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Given :-}}}$

$\large\textsf{ }$

• The ratio of the angles of the triangle are 1 : 3 : 5

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; To \; \; Find :-}}}$

$\large\textsf{ }$

• The measurement of the each Angle of the triangle = ?

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Solution :-}}}$

$\large\textsf{ }$

• We know that the sum of all the angles of the triangle is 180° .
• So let's assume the common multiple of the ratio of the given angels as x

$\large\textsf{ }$

• So the angles would be :-

1. x
2. 3x
3. 5x

__________________________________________________________

$\qquad\tt{:}\longrightarrow\large\textsf\textcolor{orange}{\; \; ∴ \; x + 3x + 5x = 180°}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; ∴ 9x = 180°}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; ∴ x = \cancel\cfrac{\large\textsf{180°}}{\large\textsf{9}} }\\\\\\\qquad\tt{:}\longrightarrow\boxed{\underline{\overline{\large\mathfrak\textcolor{red}{\; \; ∴ \; x \; = \; 20° \; }}}}$

__________________________________________________________

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{x = 20°}$

$\qquad\tt{:}\longrightarrow\large\textsf{3x = 60°}$

$\qquad\tt{:}\longrightarrow\large\textsf{5x = 100°}$

__________________________________________________________

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textbf\textcolor{magenta}{∴ The angles are 20° , 60° , 100°}}$