Question

In a triangle the largest angle is 5 degree more than 4 times its smallest angle.The other angle is twice the smallest angle.What are the 3 angles of the triangle…..?​

Answer 1

Given: In a triangle, the largest angle is five more than four times its smallest angle. & The other angle is twice the smallest angle.

Need to find: The three angles of ∆?

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❍ Let's say the smaller angle be x. Then, the largest angle and another angle would be (4x + 5) and 2x.

$\underline{\bigstar\:{\pmb{\textsf{Angle Sum Property of}} \: \sf{\Delta} \;:}}$

The ASP (Angle Sum Property) of the triangle States that the Sum of all angles of the triangle is 180°.

⠀

$:\implies{\sf{\pmb{\angle A + \angle B + \angle C = 180^\circ}}}$

$:\implies\sf x + 4x + 5 + 2x = 180^\circ$

$:\implies\sf 7x + 5 = 180^\circ$

$:\implies\sf 7x = 180^\circ - 5$

$:\implies\sf 7x = 175$

$:\implies\sf x = \cancel\dfrac{175^\circ}{7}$

$:\implies\underline{\boxed{\pmb{\frak{\purple{x = 25^\circ}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{Angles\;of\;the\:\Delta\:are\; :}}$⠀⠀⠀⠀

x = 25°

(4x + 5) = (4[25] + 5) = 105°

2x = 2(25) = 50°

⠀

$\therefore{\underline{\sf{Hence, \: the \: angles \: of \: \Delta \: are \: \pmb{ 25^\circ, \; 105^\circ,\; 50^\circ} \: respectively.}}}$

$\huge\mathtt\red{\textsf{MrUniqueBoi}}$

Answer 2

Answer:

Need to find: The three angles of ∆?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❍ Let's say the smaller angle be x. Then, the largest angle and another angle would be (4x + 5) and 2x.

$\begin{gathered}\underline{\bigstar\:{\pmb{\textsf{Angle Sum Property of}} \: \sf{\Delta} \;:}}\\\end{gathered}$

The ASP (Angle Sum Property) of the triangle States that the Sum of all angles of the triangle is 180°.

⠀

$\begin{gathered}:\implies\sf x + 4x + 5 + 2x = 180^\circ\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x + 5 = 180^\circ\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x = 180^\circ - 5\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 7x = 175\\\\\\\end{gathered}$

$\begin{gathered}:\implies\sf x = \cancel\dfrac{175^\circ}{7}\\\\\\\end{gathered}$

$\begin{gathered}:\implies\underline{\boxed{\pmb{\frak{\purple{x = 25^\circ}}}}}\;\bigstar\\\end{gathered}$

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⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Angles\;of\;the\:\Delta\:are\; :}}$

⠀⠀⠀⠀

x = 25°

(4x + 5) = (4[25] + 5) = 105°

2x = 2(25) = 50°

⠀

$\therefore{\underline{\sf{Hence, \: the \: angles \: of \: \Delta \: are \: \pmb{ 25^\circ, \; 105^\circ,\; 50^\circ} \: respectively}}}$

$\huge\mathtt\red{\textsf{MissCrispello}}$