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Q.

The diagram shows an isosceles triangle. Then the value of x ____.


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Detailed Solution

We see in the given diagram that we are given an isosceles triangle with angles subtended at the apex as 44°   and one other as x°  . We denote the apex as A, the vertex at which the unknown angle x°   is subtended as B and the third vertex as C. we have a diagram as;
Question ImageWe are give in the figure that the sides AB and AC are equal, ∠BAC=44°   and ∠ABC=x°  
We know that if measures of two angles in a triangle are equal then the length of their opposite sides is equal. Its converse is also true which means if the lengths of two sides of a triangle are equal then the measures of their opposite angles are equal. So the angles opposite to AB and AC are going to be equal which are ∠ABC = ∠ACB. So we have;
∠ABC=∠ACB=x°  
We know that the sum of the measures of angles in a triangle is  180°  . The three angles in the isosceles triangle are ∠ABC, ∠ACB, ∠BAC. So we have;
∠ABC + ∠ACB + ∠BAC = 180°  
We put previously obtained  ∠ABC=∠ACB=x°   and given  ∠BAC=44°   in the above step to have;
⇒x°+x°+44°=180° ⇒2x°+44°=180° ⇒2x°=136° ⇒x°=68°  
 
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