Question

an exterior angle of a triangle is of measure 70° and one of its interior opposite angles is of measure 25° find the measure of other interior opposite angle​

Answer 1

Given :-

• An exterior angle of a triangle is of measure 70° and one of its interior opposite angles is of measure 25°.

To Find :-

• Find the measure of other interior opposite angle​

Solution :-

~Here, we're given that an exterior angle of a triangle is of measure 70° and one of its interior opposite angles is of measure 25° and we need to find  the measure of other interior opposite angle. Firstly we'll find the interior angle which is on the linear pair with the exterior angle given to us , after finding it we can find the third interior angle by applying the angle sum property of a triangle.

_____________

Let the interior angle of the triangle be :

∠ 1

∠ 2

∠ 3

Where ,

• ∠ 1 we need to find
• ∠ 2 is in linear pair with exterior angle given to us ( 70° )
• ∠ 3 is given as 25°

As we know that ,

★ Linear pair are the pair of angles which lie on a straight line and their sum is of 180°

★ According to the angle sum property of triangles , sum of all all angles of triangle is 180°

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Finding ∠2 :-

⟶ ∠2 + 70° = 180°

⟶ ∠2 = 180° - 70°

⟶ ∠2 = 110°

[ According to linear pair ]

Finding the other interior opposite angle :-

⟶ ∠1 + ∠2 + ∠3 = 180°

⟶ ∠1 + 110°+ 25°  = 180°

⟶ 135° + ∠1 = 180°

⟶ ∠1 = 180° - 135°

⟶ ∠1 = 45°

[ According to angle sum property of triangle ]

​_____________

Hence,

• The measure of other interior opposite angle is 45°

Answer 2

Answer:

Exterior angle = 70°

One of interior opposite angles =25°

Let x be the other interior opposite angle

x+ 25° = 70° (EAP)

So x = 70°- 25°

x =45°