An exterior angle of a triangle is 105 and its two interior opposite angles are equal

Answer

Verified

Here, \[\text{In }\Delta \text{ABC, }\angle \text{ACO=}\angle \text{B+}\angle \text{A}\]We have an exterior angle equal to \[{{105}^{\circ }}\] and both interior angles are equal.Let the interior angle be x.\[\begin{align} & \Rightarrow x+x={{105}^{\circ }} \\ & \Rightarrow 2x={{105}^{\circ }} \\ \end{align}\]On dividing the equation by 2, we get:\[\begin{align} & \Rightarrow \dfrac{2x}{2}=\dfrac{{{105}^{\circ }}}{2} \\ & \Rightarrow x=52{{\dfrac{1}{2}}^{\circ }} \\ \end{align}\]Hence, each of the equal angle is \[52{{\dfrac{1}{2}}^{\circ }}\]Therefore, the correct option is B.

Note: If you do not remember the property in case you can solve it by another method in which first of all you just find the third angle of the triangle using the linear pair property by subtracting \[{{105}^{\circ }}\] from \[{{180}^{\circ }}\]. Then, use the property of a triangle i.e. the sum of internal angles of a triangle is equal to \[{{180}^{\circ }}\] to find the value of x.

लिखित उत्तर

`37(1)/(2)@` `52(1)/(2)@` `72(1)/(2)@` `75^(@)`

Answer : ```B

Solution : Let one of interior angle be `x^(@)` . `:.`"Sum of two opposite interior angles = Exterior angle" `:. " " x^(@) + x^(@) = 105^(@) " " [:. "Exteriro angle" = 105^(@)` (given)] ` rArr " " 2 x^(@) = 105 ^(@)` `:. " " x^(@) = 105^(@)/2` `rArr " " x^(@) = 52(1)/(2)@` " Hence, each angle of a triangle is" `52(1)/(2)@`

Question 3 Lines and Angles - Exercise 6.1

Answer:

(B) 52 ½o

Explanation:

According to the question,

Exterior angle of triangle= 105°

Let the two interior opposite angles of the triangle = x

We know that,

Exterior angle of a triangle = sum of interior opposite angles

Then, we have the equation,

105° = x + x

2x = 105°