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°.

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

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

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

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

$:\implies\sf 7x = 175$

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

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

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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°

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

Answer 2

Given :-

In a triangle the largest angle is 5 degree more than 4 times its smallest angle.The other angle is twice the smallest angle

To Find :-

Angles

Solution :-

Let the angles be x,y and z

x = x

z = 4x + 5

y = 2x

ATQ

x + y + z = 180

x + 4x + 5 + 2x = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25°

Hence

x = 25

y = 4x + 5 = 4(25) + 5 = 100 + 5 = 105°

z = 2x = 2(25) = 50°