Question

In a triangle ,if two of the angles are complimentry,then the measure of the third angle is

Answer 1

Question :-

• In a triangle, if two of the angles are complimentry, then the measure of the third angle is?

Answer :-

• The third angle = 90°.

Given :-

• Two angles of a triangle are complimentary.

To find :-

• The measure of third angle.

Solution :-

We know that two angles of the triangle are complimentary.

We are asked to find the third angle.

We know that, The sum of two complimentary angles is 90°.

$\sf Let \: two \: complimentary \: angles \: be \: \begin{cases} \sf x \\ \sf y\end{cases}$

So, The equation will be :- (Eq - 1)

$\sf x + y= 90 \degree$

And also, Let us assume third angle as z.

• And, We also know that, Sum of all angles of a triangle is equal to 180°

Now, The equation will be :- (Eq - 2)

$\sf x + y + z= 180 \degree$

Putting the values of equation 1,

$\sf 90\degree+ z= 180 \degree$

Transposing 90° from LHS to RHS, Changing the sign from (+) to (-)

$\sf z= 180 \degree - 90\degree$

$\sf z= 90 \degree$

Therefore, The measure of third angle is 90°.

Answer 2

Answer:

The third angle will be of 90°