Question

Question 57

Fill in the blanks to make the statement true.

If one angle of a triangle is equal to the sum of other two, then the measure of that angle is ___

Answer 1

Let the angles of a triangle be a, b and c. It is given that,
a = b + c
We also know that, $a+b+c={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow a+a={180}^{\circ }$ $[\because b+c=a]$
$\Rightarrow 2a={180}^{\circ }\Rightarrow a=\frac{{180}^{\circ }}{2}\Rightarrow a={90}^{\circ }$
Hence, the measure of that angle is ${90}^{\circ }$