Question

An exterior angle of a triangle measure 110° and its interior opposite angle are in the ratio2:3 . Find the measure of the triangle​

Answer 1

here is your answer dude....

Answer 2

$\red\bigstar$ Correct Question:

• An exterior angle of a triangle measure 110° and its interior opposite angle are in the ratio2 : 3 . Find the measure of the interior opposite angles of the triangle.

$\pink\bigstar$Answer:

• 44°
• 66°

$\blue\bigstar$ Given:

• The exterior angle of the triangle is 110°.
• The ratio of the interior opposite angles is 2 : 3

$\green\bigstar$To find:

• The measure of the interior opposite angles.

$\red\bigstar$ Solution:

Let the interior opposite angles be in the form of x.

$\therefore$The interior opposite angles are :

$\hookrightarrow$ 2x

$\hookrightarrow$ 3x

Now we know that :

• Exterior angle = Sum of both the opposite interior angles

$\therefore$ 110° = 2x + 3x

[ By substituting their values ]

$\implies$ 5x = 110°

$\implies$ x = $\dfrac{{110}^{\circ}}{5}$

$\implies$x = 22°

Now,

$\hookrightarrow$ 2x

= 2 × 22°

= 44°

$\hookrightarrow$ 3x

= 3 × 22°

= 66°

$\therefore$ The angles are 44° and 66°.

$\pink\bigstar$ Concepts Used:

• Exterior angle Property Of A Triangle
• Assumption of values in variables
• Substitution of values

$\blue\bigstar$Extra - Information:

• The sum of all the interior angles of a triangle is 180°
• Corresponding angles formed by the intersection of a transversal with parallel lines are equal.
• Sum of co-interior angles is 180°
• Alternate interior angles are equal
• Exterior opposite angles are equal
• A linear pair consisting of adjacent supplementary angles, sum is 180°.
• The sum of complementary angles is 90°
• The sum of Supplementary angles is 180°