Question

an exterior angle of a triangle is 125° and
its interiore opposite angles are equal, then find the measures of each equal angles​

Answer 1

Step-by-step explanation:

As we know the sum of two interior opposite angles is equal to exterior angle.

Let the angles be x and 4x.

so,

x+4x=125

5x=125

x=125/5

x=25

Therefore,

1st angle is x=25 degrees

2nd angle is 4x=4∗25=100 degrees.

Answer 2

$\blue\bigstar$Answer:

$\sf\: \boxed{x \: = \: {62.5}^{ \circ}}$

$\pink\bigstar$Given:

• The exterior angle of the triangle = 125°
• Interior Opposite angles are equal.

$\red\bigstar$ To find:

• The measure of each Angle.

$\blue\bigstar$ Solution:

Let the triangle be $\triangle$ABC and each interior opposite angle be x.

We know that:

• The exterior angle of the triangle = Sum of both the interior opposite angles

$\therefore$ $\angle$CAB + $\angle$ABC = $\angle$ACD

( The exterior angle of the triangle is equal to sum of both the interior opposite angles )

$\implies$ x + x = 125°

( Substituting the Values )

$\implies$ 2x = 125°

$\sf\implies x \: = \: \cancel {\dfrac {{125}^{ \circ}}{2}}$

$\sf\implies \: \boxed{x \: = \: {62.5}^{ \circ}}$

$\therefore$ each of the interior opposite angle is 62.5°

$\pink\bigstar$ Concepts Used:

• Assumption of unknown angle
• Exterior angle Property Of A Triangle
• Substitution of values

$\red\bigstar$Extra - Information:

• The sum of all angles in a triangle is 180°
• If two sides of a triangle are unequal, the angle opposite to the longer side is greater.
• The sum of any two sides of a triangle is greater than the third side.