Question

Q15. Two angles of a triangle are in the ratio 1:2 If the sum of these angles is equal to
the third angle, Find the angles of the triangle. What type of triangle is it? Also classily
the triangle as acute, obtuse, right, Scalene, isosceles or equilateral.
016 Find the smallest three dimit um​

Answer 1

ATQ, the ratio of two angles of the triangle are in ratio 1 : 2 and the third angle is equal to the sum of first two angles.

let the first two angles be 1x and 2x.

therefore third angle = x + 2x = 3x

we know that the sum of angles of a triangle is 180°

➡ x + 2x + 3x = 180°

➡ 6x = 180°

➡ x = 180/6

➡ x = 30°

hence, the angles are :-

• x = 30°
• 2x = 2 × 30 = 60°
• 3x = 3 × 30 = 90°

the triangle is a right angle triangle since it's third angle is equal to 90°

also it's a scalene triangle.

Answer 2

$\large{\mathfrak{\underline{\underline{Solution:-}}}}$

____________________

Let the angles be 1x (also, x) and 2x

[according to their ratios]

Therefore, third side would be

x + 2x = 3x

As we know, [the sum of the angles of a triangle is = 180°

Then, ATQ

$\large{\boxed{x + 2x + 3x = 180°}}$

$\large{ ⇒ 6x = 180°}$

$\large{⇒ x = \frac{180°}{6} }$

$\large{\boxed{\red{x = 30°}}}$

Thus, the angles are

x = 30°

2x = 2×30 = 60°

3x = 3×30 = 90°

Since, sum of first and second angle is equal to its third angle i.e 90° (30°+60°)

Therefore, it is a Right angle triangle with all unequal sides i.e scalene triangle.