Question

of the three angles of a triangle,the second one is one third of the first abd the third angle is 26 dgrees mote than the first angle. find all the three angles of the triangle​

Answer 1

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Let's solve the problem now!!!

$\green{\large\underline{\bf{Solution-}}}$

Given that, 3 angles of a triangle such that

• second angle is one third of the first angle

• third angle is 26° more than the first angle

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{first \: angle = 3x} \\ &\sf{second \: angle = x}\\ &\sf{third \: angle = 3x + 26} \end{cases}\end{gathered}\end{gathered}$

We know that,

• Sum of interior angles of a triangle is 180°.

Therefore,

$\rm :\longmapsto\:3x + x + 3x + 26 = 180$

$\rm :\longmapsto\:7x + 26 = 180$

$\rm :\longmapsto\:7x = 180 - 26$

$\rm :\longmapsto\:7x = 154$

$\bf\implies \:x = 22$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{first \: angle = 3x = 22 \times 3 = 66} \\ &\sf{second \: angle = 22}\\ &\sf{third \: angle = 3x + 26 = 66 + 26 = 92} \end{cases}\end{gathered}\end{gathered}$