Question

What angle measure is supplementary to 69?

Answer 1

Hint:We need to use the concept of supplementary angles in mathematics. Two angles x and y are said to be supplementary is their sum is equal to $180{}^\circ .$ This can be represented as $x+y=180{}^\circ .$ This means that the supplementary angle for x is y and for y is x. We use this concept to solve the above problem. We subtract the above angle from $180{}^\circ $ and obtain the answer in degrees.

Complete step by step answer:
In order to solve this question, let us represent the concept of supplementary angles in the form of an equation. This can be given by $x+y=180{}^\circ .$ Thus we can say that angle x is the supplementary angle of y and vice versa. According to the question, we can see that one angle is given as $69{}^\circ .$ Let us assume this is x and substitute in the equation and find its supplementary angle y by subtracting with $180{}^\circ .$
Let $x=69{}^\circ ,$
$\Rightarrow x+y=180{}^\circ $
Substituting for x as $69{}^\circ ,$ we shall calculate for the value of y.
$\Rightarrow 69{}^\circ +y=180{}^\circ $
Subtracting both sides of the equation by $69{}^\circ ,$
$\Rightarrow y=180{}^\circ -69{}^\circ $
Subtracting the two terms in the right-hand side,
$\Rightarrow y=111{}^\circ $
We have obtained the supplementary angle for $69{}^\circ .$

Hence, $111{}^\circ $ is the angle supplementary to the angle $69{}^\circ .$

Note: We need to know the concept of complementary and supplementary angles in mathematics. We have explained the concept of supplementary angles in the problem given above. Complementary angles means that the sum of the two angles add up to $90{}^\circ .$ This needs to be known by students in order to easily solve such sums.