Question

One angle of a triangle is 70 and the other two angles are in the ratio 5:6.Find these angles.​

Answer 1

$\star \; {\underline{\boxed{\pmb{\green{\frak{ \; Given \; :- }}}}}}$

• $\sf{ \angle 1 = 70^{ \circ } }$
• The other two angles are in the ratio 5:6

$\star \; {\underline{\boxed{\pmb{\pink{\frak{ \; To \; Find \; :- }}}}}}$

• Find the Other two angles

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\pmb{\purple{\frak{ \; SolutioN \; :- }}}}}}$

❖ ${\underline{\underline{\sf{ \; We \; Know \; That \; :- }}}}$

• Sum of Angles(Triangle) = 180°

❖ ${\underline{\underline{\sf{ \; Let \; the \; Ratios \; :- }}}}$

• $\sf{ \angle 2 = 5y^{ \circ } }$
• $\sf{ \angle 3 = 6y^{ \circ } }$

❖ ${\underline{\underline{\sf{ \; Calculating \; the \; Value \; of \; y \; :- }}}}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { \angle 1 + \angle 2 + \angle 3 = 180^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { 70^{ \circ } + 5y^{ \circ } + 6y^{ \circ } = 180^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { 70^{ \circ } + 11y^{ \circ } = 180^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { 11y^{ \circ } = 180^{ \circ } - 70^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { 11y = 110 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { y = \dfrac{110}{11} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; \sf { y = \cancel\dfrac{110}{11} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \qquad \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak { y = 10 }}}}} \; \red{\pmb{\dag}} \\ \\ \\ \end{gathered}$

❖ ${\underline{\underline{\sf{ \; Calculating \; the \; Angles \; :- }}}}$

• $\sf{ \angle 2 }$ = 5y = 5(10) = 50°
• $\sf{ \angle 3 }$ = 6y = 6(10) = 60°

$\therefore \;$ The two angles are 50° and 60° .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

$\Large\bigstar \; {\underline {\boxed {\pmb{\red{\frak{ \; Question \; :- \: }}}}}}$

• One angle of a triangle is 70 and the other two angles are in the ratio 5:6.Find these angles.

$\Large\bigstar \; {\underline {\boxed {\pmb{\red{\frak{ \; Answer \; :- \: }}}}}}$

• Angle 2 = 50°
• Angle 3 = 60°

$\Large\bigstar \; {\underline {\boxed {\pmb{\purple{\frak{ \; Given \; :- \: }}}}}}$

• One angle of triangle = 70°
• Ratio = 5:6

$\Large\bigstar \; {\underline {\boxed {\pmb{\purple{\frak{ \; Using \; Formula :- \: }}}}}}$

• Angles sum property of triangle = 180°

$\Large\bigstar \; {\underline {\boxed {\pmb{\purple{\frak{ \; Proving \; of \; Formula :- \: }}}}}}$

• Here, To prove the formula we are using we can do it in the following way.
• To find the angle sum property of any polygon we use the following method.
• $\mapsto$$\sf\bold{ (2n-4) \times right \: angle}$
• $\mapsto$$\sf\bold{ (2 \times 3 \: - 4) \times 90}$
• $\mapsto$$\sf\bold{ (6 \: - 4) \times 90}$
• $\mapsto$$\sf\bold{ 2 \: \times 90}$
• $\mapsto$$\sf\red{180°}$
• Here, n = No. of sides

$\Large\bigstar \; {\underline {\boxed {\pmb{\purple{\frak{ \; Explanation \; :- \: }}}}}}$

• Angle 1 = 70°
• Ratio given = 5:6
• Let us assume Angle 2 = 5x
• Therefore, Angle 3 = 6x
• Now, we can easily find the two other angles of triangle by using the formula given above.

$\Large\bigstar \; {\underline {\boxed {\pmb{\purple{\frak{ \; Solution \; :- \: }}}}}}$

• Angle sum property of triangle = 180°
• $\mapsto$Angle 1 + Angle 2 + Angle 3 = 180°
• $\mapsto$70° + 5x + 6x = 180°
• $\mapsto$11x = 180 - 70
• $\mapsto$ 11x = 110°
• $\mapsto$$\sf{x \: = \: \cancel\dfrac{110}{11}}$
• $\mapsto$$\sf\red{x \: = \: 10°}$

$\Large\bigstar \; {\underline {\boxed {\pmb{\pink{\frak{\; Final \; Answer :- \: }}}}}}$

• $\mapsto$Angle 1 = 70°
• $\mapsto$Angle 2 = 5x => 5 x 10
• $\mapsto$$\sf\red{50°}$
• $\mapsto$Angle 3 = 6x => 6 × 10
• $\mapsto$$\sf\red{60°}$