Question

In a triangle largest angle is 20 degree more than the smallest angle.The third angle is 10 degree more than the smallest angle.What is the sum of angles in a triangle?What is the measures of angles in a triangle?​

Answer 1

Answer:

1 angle be x then it will be x + 20

2 angle be x + 10

smallest angle be x

x + 20 + x + 10 + x = 180

3x + 30 = 180

3x = 180 - 30

3x = 150

x = 150/ 3

x = 50

smallest angle = 50

third angle = 50 + 10 = 60

largest angle = 50 + 20 = 70

Answer 2

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

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