Question

In a pair of supplementary angles, the greater angle exceeds the smaller by $50^\circ$. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

Hint:

Translate real-life conditions into linear equations for systematic solving.

Answer 1

Problem:
Two angles are supplementary and one angle is 50° more than the other. Find both angles.

Step 1: Let the smaller angle be \( x^\circ \)
Then, the greater angle will be \( x + 50^\circ \)

Step 2: Use the condition for supplementary angles
Supplementary angles add up to \( 180^\circ \). So: \[ x + (x + 50) = 180 \quad \text{(Equation 1)} \]
Step 3: Simplify the equation
\[ x + x + 50 = 180\\ 2x + 50 = 180 \]
Step 4: Solve for \( x \)
\[ 2x = 180 - 50 = 130\\ x = \frac{130}{2} = 65 \]
Step 5: Find the greater angle
\[ y = x + 50 = 65 + 50 = 115 \]
Final Answer:
Smaller angle = \( \boxed{65^\circ} \)
Greater angle = \( \boxed{115^\circ} \)