Question

In \[\vartriangle ABC\], \[AB = AC\] and \[\angle A = {60^ \circ }\]. Draw it Also, measure the angle \[\angle B\] and \[\angle C\].

Answer 1

Hint: Here in this question, given a triangle ABC and its side \[AB = AC\] and \[\angle A = {60^ \circ }\] we need to find angle \[\angle B\] and \[\angle C\]. For this, first we need to draw a triangle and after we have to measure an angle \[\angle B\] and \[\angle C\] by using a protractor otherwise we can also find the angle \[\angle B\] and \[\angle C\] by using the sum of triangle interior angles and by isosceles property.

Complete step by step answer:
Isosceles triangle is a type of triangle which has any two of its sides equal to each other and also, the angles opposite these equal sides are equal. Consider a given question: Draw a triangle \[\vartriangle ABC\], the two sides AB and AC are equal, \[AB = AC\] and angle \[\angle A = {60^ \circ }\].

In the above triangle the side AB and AC are equal it means the triangle \[\vartriangle ABC\] is a isosceles triangle, then we use the protractor to measure an angle of \[\angle B\] and \[\angle C\] it measures an angle \[{60^ \circ }\]i.e., \[\angle B = \angle C = {60^ \circ }\].
Otherwise, the \[\vartriangle ABC\] is a isosceles triangle,
Since, the side \[AB = AC\] and \[\angle A = {60^ \circ }\].
We need to find whether \[\angle B = \angle C = \],
As we know that, angles opposite to equal sides of an isosceles triangle are equal, then
Let’s consider \[\angle B = \angle C = x\]. We know that, the sum of the interior angles of a triangle equals \[{180^ \circ }\]. In triangle \[\vartriangle ABC\],
\[ \Rightarrow \,\,\,\,\angle A + \angle B + \angle C = {180^ \circ }\]
\[ \Rightarrow \,\,\,\,{60^ \circ } + x + x = {180^ \circ }\]
\[ \Rightarrow \,\,\,\,{60^ \circ } + 2x = {180^ \circ }\]
Subtract both side by \[{180^ \circ }\], then
\[ \Rightarrow \,\,\,\,2x = {180^ \circ } - {60^ \circ }\]
\[ \Rightarrow \,\,\,\,2x = {120^ \circ }\]
Divide both side by 2, then
\[ \Rightarrow \,\,\,\,x = {\dfrac{{120}}{2}^ \circ }\]
On simplification, we get
\[\therefore \,\,\,x = {60^ \circ }\]

Hence, in \[\vartriangle ABC\] the angle \[\angle B = \angle C = {60^ \circ }\].

Note: While solving these type of questions, we have to know the definition of types of triangle equilateral triangle, isosceles triangle and right angled triangle and know some basic properties, Axiom and postulates of triangle like in isosceles triangle two sides are always equal and the angles opposite these equal sides are equal.