Question

one side of triangle is produced making an exterior angle of measure 126° if the interior opposite angles are in ratio 2:5 find the measure if each angle of the triangle what kind of triangle it is?​

Answer 1

Question :-

• One side of triangle is produced making an exterior angle of measure 126° if the interior opposite angles are in ratio 2:5. Find the measure of each angle of the triangle and what kind of triangle it is?

Given :-

• One side of triangle is produced making an exterior angle of measure 126°.
• The interior opposite angles are in ratio 2:5.

To Find :-

• The measure of each angle of the triangle.
• What kind of triangle it is?

Solution :-

Since, the interior opposite angles are in ratio 2:5.

Let interior opposite angles be 2x and 5x respectively.

Using properties of exterior angle of a triangle that exterior angle of a triangle is equals to sum of interior opposite angles.

$\begin{gathered}\bf\pink{Now} \end{gathered}$

$\bf \:  ⟼ 5x + 2x = 126$

$\bf \:  ⟼ 7x = 126$

$\bf \:  ⟼ x = \dfrac{126}{7}$

$\bf \:  ⟼ x = 18$

So,

$\bf \:⟼First \: interior \: angle = 2x = 2 \times 18 = 36$

$\bf \:  ⟼ Second \:interior \: angle = 5 \times 18 = 90$

$\bf \:  ⟼ Third \:angle = 180 - 90 - 36 = 54$

So,

$\large \red{\bf \:  ⟼ Triangle \: is \: right \: angle \:∆.} ✍$

___________________________________________

$\large \red{\bf \: ⟼ Explore \: more } ✍$

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.