Question

Angles of a triangle are (x+100), (x+400) and (2x-300). What is the value of x?​

Answer 1

Answer:

x=127

Step-by-step explanation:

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Answer 2

$\begin{gathered}\begin{gathered}\bf Given \:angles \: of \: \triangle \: are - \begin{cases} &\sf{(x + 10) \degree \: } \\ &\sf{(x + 40)\degree \:} \\ &\sf{(2x - 30)\degree \:} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \: Find \: -   \begin{cases} &\rm{value \: of \: x}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

We know,

• Sum of angles of a triangle is 180°.

$\rm : \implies \:x + 10 + x + 40 + 2x - 30 = 180$

$\rm : \implies \:4x + 20 = 180$

$\rm : \implies \:4x = 180 - 20$

$\rm : \implies \:4x = 160$

$\rm : \implies \:x = 40$

$\begin{gathered}\begin{gathered}\bf \therefore \:angles \: of \: \triangle \: are - \begin{cases} &\sf{(40 + 10) \degree \: = 50\degree \:} \\ &\sf{(40 + 40)\degree \: = 80\degree \:} \\ &\sf{(2 \times 40 - 30)\degree \: = 50\degree \:} \end{cases}\end{gathered}\end{gathered}$

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Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.