Finding Two Supplementary Angles

Video Explanation

Question

The larger of two supplementary angles exceeds the smaller by 18°. Find the two angles.

Solution

Step 1: Concept

Sum of supplementary angles = \(180^\circ\)

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Step 2: Let Variables

Let smaller angle = \(x^\circ\)

Let larger angle = \(y^\circ\)

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Step 3: Form Equations

Sum condition:

\[ x + y = 180 \quad (1) \]

Difference condition:

\[ y – x = 18 \quad (2) \]

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Step 4: Solve Linear Equations

Add (1) and (2):

\[ 2y = 198 \Rightarrow y = 99 \]

Then:

\[ x = 180 – 99 = 81 \]

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Step 5: Final Answer

\[ \text{Smaller angle} = 81^\circ,\quad \text{Larger angle} = 99^\circ \]

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Verification

Sum: \(81 + 99 = 180^\circ\) ✔

Difference: \(99 – 81 = 18^\circ\) ✔