Question

Find the value of x in the following figure. Do not give wrong answer

Answer 1

Let us name the triangle as ABC (refer the pic that I provided)

So we know that angle BAC and 110° are linear pair.

This means their sum is 180°

So the equation is,

110° + angle BAC = 180°

=> angle BAC = 180 - 110

=> angle BAC = 70°

It is shown in the pic that two sides are equal. Hence the third angle would be equal to x

So we have 70° + x + x = 180° (angle sum property of triangle)

=> 2x + 70° = 180°

=> 2x = 180° - 70°

=> 2x = 110°

=> x = 110/2

=> x = 55°


Hence your answer is 55°


Hope it helps dear friend ☺️✌️

Answer 2

Heya!!

Thanks for asking the question!

Answer : x = 55°

Explanation :

Things to know first before coming to the main solution :

What is a triangle?
- A triangle is a three sided closed polygon whose sum of interior angles is 180° ( from (n-3)180° where n is no. of sides of polygon) and sum of all exterior angles is equal to 360°

There are three types of triangle on the basis of sides -

1) Equilateral triangle ( all sides equal )
2) Isosceles triangle ( any two sides equal )
3) Scalene triangle ( all three sides unequal)

There are three types of triangles on the basis of measures of its interior angles. They are as follows -

1) Acute angled triangle ( all angles are acute angles)
2) Obtuse angled triangle ( one interior angle is obtuse angle)
3) Right angled triangle ( one angle equal to right angle. )


Theorem 1 - Sides opposite to equal angles in a triangle are equal .

Theorem 2 ( Converse of theorem 1) - Angles opposite to equal sides in a triangle are equal.


What is an isosceles triangle?
- A isosceles triangle is a type of triangle whose two sides are equal and angles opposite to equal sides are equal.


Exterior angle property - This property states that in any triangle sum of any two interior angles is equal to the exterior angle adjacent to the third side.

Main solution :

Given,

angle CAD = 110°,

angle ABC = x, and

AB = AC

To find ,

x

Since AB = AC,

angle ACB = angle ABC = x ( By theorem 2 )

Since angle CAD is exterior angle adjacent to angle BAC,

x + x = 110° ( By exterior angle property )

Now this is a linear equation ( degree 1 ) in one variable.

Now let's solve for x by using the method of transposition.

The steps are as follows -

2x = 110°



=> x = 55°. ( Answer )




Hope it helps you : )