Question

The measure of an angle which is 9 times its supplement is?

Answer 1

Hint:
Supplementary angles are the two angles or more than two angles with a sum of \[{180^ \circ }\]. Supplement of an angle is what, when added to it, equals\[{180^ \circ }\].
Complementary angles are the two angles or more than two angles with a sum of \[{90^ \circ }\]. Complement of an angle is what, when added to it, equals\[{90^ \circ }\].

Complete step by step solution:
Let the required angle be x.
According to question, the angles is 9 times its supplement
\[ \Rightarrow x = 9({180^ \circ } - x)..........Eq:01\]
\[ \Rightarrow x = {1620^ \circ } - 9x\]
\[ \Rightarrow x + 9x = {1620^ \circ }\]
\[ \Rightarrow 10x = {1620^ \circ }\]
\[ \Rightarrow x = {162^ \circ }\]

So, the measure of an angle which is 9 times its supplement is \[{162^ \circ }\].

Note:
Student’s can verify their answers by putting it in the Eq:01.
\[
   \Rightarrow {162^ \circ } = 9({180^ \circ } - {162^ \circ }) \\
   \Rightarrow {162^ \circ } = 9({18^ \circ }) \\
   \Rightarrow {162^ \circ } = {162^ \circ } \\
\]