write mode of the following 2 3 5 9 8 3 6 7 3 4 5 3
Answers
Answer:
We've to find out the Greatest angles of the given triangle. First We'll find all three angles of the triangle. & to find angles we'll use Angle sum property of triangle i.e (∠A + ∠B + ∠C = 180°).
So Let's Consider the angles of a triangle be 5x, 3x and 7x respectively.
⠀
\begin{gathered}\bf{\dag}\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}
†
Asweknowthat,
Sum of all angles of a triangle is 180°.
⠀
\begin{gathered}:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ\\ \\\end{gathered}
:⟹∠A+∠B+∠C=180
∘
\begin{gathered}\sf Here \begin{cases} & \sf{\angle\:A = \bf{5x}} \\ & \sf{\angle\:B = \bf{3x}} \\ &\sf{\angle\:C = \bf{7x}}\end{cases}\\\\\end{gathered}
Here
⎩
⎪
⎪
⎨
⎪
⎪
⎧
∠A=5x
∠B=3x
∠C=7x
\begin{gathered}\bf{\dag}\;{\underline{\frak{ Substituting\:values,}}}\\ \\\end{gathered}
†
Substitutingvalues,
\begin{gathered}:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ\\\\\\:\implies\sf 5x + 3x + 7x = 180^{\circ}\\\\\\:\implies\sf 15x = 180^\circ\\\\\\:\implies\sf x = \cancel\dfrac{180^\circ}{15}\\\\\\:\implies\underline{\boxed{\pmb{\frak{\pink{x = 12}}}}}\;\bigstar\\\end{gathered}
:⟹∠A+∠B+∠C=180
∘
:⟹5x+3x+7x=180
∘
:⟹15x=180
∘
:⟹x=
15
180
∘
:⟹
x=12
x=12
★
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Therefore, Angles of ∆ are :
⠀
5x = 5(12) = 60°
3x = 3(12) = 36°
7x = 7(12) = 84°
⠀
\therefore\:{\underline{\sf{Measure\: of\; Greatest\: angle\:of\:a\:\triangle\:is\:{\sf{\pmb{Option\;c)\;84^\circ}.}}}}}∴
MeasureofGreatestangleofa△is
Optionc)84
∘
Optionc)84
∘
.