Question

One of the supplementary angles exceeds the other by 120°. Express this as a system of linear equations and find the angles.

Hint:

"Supplementary" means sum to 180°, while "Complementary" means sum to 90°. A quick way to remember: 'C' comes before 'S', and 90 comes before 180.

Answer 1

Concept Used:
Supplementary angles are two angles whose sum is $180^\circ$. We form linear equations based on the given conditions and solve them simultaneously.

Step 1: Forming the System of Linear Equations
Let the two angles be $x$ and $y$.

Since they are supplementary:
\[ x + y = 180 \]
Given that one angle exceeds the other by $120^\circ$:
\[ x - y = 120 \]
Thus, the required system of linear equations is:
\[ x + y = 180 \] \[ x - y = 120 \]

Step 2: Solving the System
Add both equations:
\[ (x + y) + (x - y) = 180 + 120 \]
\[ 2x = 300 \]
\[ x = 150 \]
Substitute $x = 150$ into first equation:
\[ 150 + y = 180 \]
\[ y = 30 \]

Final Answer:
The two supplementary angles are $150^\circ$ and $30^\circ$.