Answer
396.9k+ views
Hint:
Here we will first find the value of another interior angle by using the concept of the exterior angle property of the triangle. Then by using the sum of the angles of the triangle, we will find out the value of the third angle of the triangle.
Complete step by step solution:
It is given that the exterior angle of a triangle is \[110^\circ \] and one of the interior opposite angles is \[30^\circ \].
So we will draw the diagram of the triangle using the given information.
Then by using the concept of the exterior angle property of the triangle, we get
\[\angle A + \angle B = 110^\circ \]
It is given that the angle A is \[30^\circ \]. Then by putting the value of A in the above equation, we get
\[ \Rightarrow 30^\circ + \angle B = 110^\circ \]
Subtracting \[30^\circ \] from both sides, we get
\[ \Rightarrow \angle B = 110^\circ - 30^\circ \]
\[ \Rightarrow \angle B = 80^\circ \]
We know that the sum of all the angles of a triangle is equal to \[180^\circ \]. Therefore, we get
\[\angle A + \angle B + \angle C = 180^\circ \]
By putting the value of angle A and angle B, we get
\[ \Rightarrow 30^\circ + 80^\circ + \angle C = 180^\circ \]
Adding the terms, we get
\[ \Rightarrow 110^\circ + \angle C = 180^\circ \]
Subtracting the terms, we get
\[ \Rightarrow \angle C = 180^\circ - 110^\circ \]
\[ \Rightarrow \angle C = 70^\circ \]
Hence, the value of the remaining angles of the triangle is \[80^\circ \] and \[70^\circ \].
Note:
Here we need to keep in mind the exterior angle property of the triangle. It states that an exterior angle of a triangle is always equal to the sum of the two opposite interior angles of the triangle. Vertically Opposite Angles (vertical angles) are the angles opposite each other when two lines intersect or cross each other and pairs of vertically opposite angles (vertical angles) are always equal to each other. We should know that the corresponding angles are the angles which are formed at the corresponding corners when the transversal line is passed through the two parallel lines.
Here we will first find the value of another interior angle by using the concept of the exterior angle property of the triangle. Then by using the sum of the angles of the triangle, we will find out the value of the third angle of the triangle.
Complete step by step solution:
It is given that the exterior angle of a triangle is \[110^\circ \] and one of the interior opposite angles is \[30^\circ \].
So we will draw the diagram of the triangle using the given information.
![seo images](https://www.vedantu.com/question-sets/b1b054d6-d839-424d-a7bc-72a7d76378df8223210449922063324.png)
Then by using the concept of the exterior angle property of the triangle, we get
\[\angle A + \angle B = 110^\circ \]
It is given that the angle A is \[30^\circ \]. Then by putting the value of A in the above equation, we get
\[ \Rightarrow 30^\circ + \angle B = 110^\circ \]
Subtracting \[30^\circ \] from both sides, we get
\[ \Rightarrow \angle B = 110^\circ - 30^\circ \]
\[ \Rightarrow \angle B = 80^\circ \]
We know that the sum of all the angles of a triangle is equal to \[180^\circ \]. Therefore, we get
\[\angle A + \angle B + \angle C = 180^\circ \]
By putting the value of angle A and angle B, we get
\[ \Rightarrow 30^\circ + 80^\circ + \angle C = 180^\circ \]
Adding the terms, we get
\[ \Rightarrow 110^\circ + \angle C = 180^\circ \]
Subtracting the terms, we get
\[ \Rightarrow \angle C = 180^\circ - 110^\circ \]
\[ \Rightarrow \angle C = 70^\circ \]
Hence, the value of the remaining angles of the triangle is \[80^\circ \] and \[70^\circ \].
Note:
Here we need to keep in mind the exterior angle property of the triangle. It states that an exterior angle of a triangle is always equal to the sum of the two opposite interior angles of the triangle. Vertically Opposite Angles (vertical angles) are the angles opposite each other when two lines intersect or cross each other and pairs of vertically opposite angles (vertical angles) are always equal to each other. We should know that the corresponding angles are the angles which are formed at the corresponding corners when the transversal line is passed through the two parallel lines.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)