Question

Two angles of a triangle are the ratio 1:2. If the
third angle is equal to the sum of the other two find
the three angles of the triangle​

Answer 1

GiveN :

• Two angles of triangle are 1:2.
• Third angle is sum of other two angles.

To FinD :

• Find all the angles

SolutioN :

Let two angles be : 1x and 2x

Then third angle will be 1x + 2x

Use Angle sum property of Triangle :

⇒Sum of all angles = 180°

⇒1x + 2x + 1x + 2x = 180°

⇒2x + 4x = 180°

⇒6x = 180°

⇒x = 180°/6

⇒x = 30°

______________________

Now, all the angles are :

• First Angle = x = 30°

• Second Angle = 2x = 2(30°) = 60°

• Third Angle = 1x + 2x = 3x = 3(30°) = 90°

________________________

Proof :

⇒Sum of Angles = 180°

⇒30° + 60° + 90° = 180°

⇒90° + 90° = 180°

⇒180° = 180°

$\therefore$ Hence Proved

Answer 2

Answer

The three angles of triangle are of 30° , 60° and 90° respectively

$\bf \large{ \underline{Given : }}$

• Two angles of a triangle are in the ratio 1:2
• The third angle is equal to the sum of the other two

$\bf \large \underline{To \: Find : }$

• The three angles of a triangle

$\bf \large \underline{Solution : }$

Let us consider the angles of the triangle be a , b and c

$\sf \underline{\underline{ \dag \: \: According \: to \: question : }}$

$\sf a :b = 1 : 2 \\ \\ \implies \sf\dfrac{a}{b} = \dfrac{1}{2} \\ \\ \sf\implies \dfrac{a}{b} = \dfrac{1}{2} = x \: \: \: (let) \\ \\ \implies \sf \frac{a}{1} = \dfrac{b}{2} = x \\ \\ \therefore \: \sf a = x \: \: and \: \: b = 2x$

$\sf \underline{ \underline{ \dag \: \: Again \: by \: question : }}$

$\sf c = a + b \\ \\ \sf\implies c = x + 2x \\ \\ \implies \sf c = 3x$

Now we have from properties of triangle :

$\sf sum \: of \: all \: angles \: of \: triangle = 180 \degree \\ \\ \sf\implies a + b + c = 180 \degree \\ \\ \sf \implies x + 2x + 3x =180 \degree \\ \\ \implies \sf 6x =180 \degree \\ \\ \sf \implies x = \dfrac{ \cancel{180} \degree}{\cancel{6}} \\ \\ \implies \sf x = 30\degree$

Therefore , all the three angles are : 30° , 60° and 90° respectively