Question

if an exterior angle of a triangle is 120' and one of the interior opposite angle is 50. find the other interior opposite angle​

Answer 1

Answer:

Step-by-step explanation:

ANSWER

Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.

Let ΔABC be a triangle where the side BC is produced.

By the theorem we have

∠A+∠B=100  

o

 …………..(1)

It is given that the interior opposite angles are equal i.e., ∠A=∠B.

∴ Equation (1) becomes

2∠A=100  

o

 

⇒∠A=50  

o

 

⇒∠B=50  

o

 

Using angle sum property of a triangle,

Sum of all angles of a triangle =180  

o

 

⇒∠A+∠B+∠C=180  

o

 

⇒100+∠C=180  

o

 [from (1)]

⇒∠C=180  

o

−100  

o

 

⇒∠C=80  

o

.

Hence ∠A=50  

o

 

∠B=50  

o

 

∠C=80  

o

.

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Answer 2

• Other interior angle is 70°.

Step-by-step explanation:

To find:-

• Other interior angle of triangle.

Solution:-

Let, Other interior angles be ∠1 and ∠2.

By First method:-

We know that,

Sum of all angles forms on straight line is equal to 180°. This statement is known as linear pair.

So,

➝ ∠2 + 120° = 180°

➝ ∠2 = 180° - 120°

➝ ∠2 = 60°

We also know that,

Sum of all interior angles of triangle is 180°. This statement is known as 'Angle sum property of triangle'.

So,

➝ ∠1 + 50° + ∠2 = 180°

➝ ∠1 + 50° + 60° = 180°

➝ ∠1 + 110° = 180°

➝ ∠1 = 180° - 110°

➝ ∠1 = 70°

Other angle of triangle is 70°.

By second method:-

We know that,

Sum of any two interior angles of triangle is equal to one opposite exterior angle.

➝ ∠1 + 50° = 120°

➝ ∠1 = 120° - 50°

➝ ∠1 = 70°

Other interior angle of triangle is 70°.