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

Answer:

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.

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

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

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

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

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

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

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

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

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

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x = 25°

(4x + 5) = (4[25] + 5) = 105°

2x = 2(25) = 50°

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

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

Answer 2

• Let the smaller angle be = x
• Given Largest angle is 5 more than four times smalles angle
• Four times smaller angle = 4 * x = 4x

Largest angle = 5 + 4x (given)

3rd angle = 2 * x ( smaller angle) = 2x

1st angle = x

2nd angle = 5 + 4x

3rd angle = 2x

Sum of angles in a triangle = 180 degrees

x + 5 + 4x + 2x = 180 deg

7x + 5 = 180

7x = 180 -5

7x = 175

x = 175/7 = 25 degrees

1st angle = x = 25degrees

2nd angle = 5 + 4( 25) = 105 degrees

3rd angle = 2 * 25 = 50 degrees