Question
The measure of angle is \( 107^{\circ} \). What is the measure of its supplementary angle?
Ask by Chadwick Pena. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The supplementary angle is \(73^\circ\).
Solution
**Step 1:**
By definition, two angles are supplementary if the sum of their measures is \(180^\circ\).
**Step 2:**
Let the measure of the supplementary angle be \(x\). Then,
\[
107^\circ + x = 180^\circ
\]
**Step 3:**
To find \(x\), subtract \(107^\circ\) from both sides:
\[
x = 180^\circ - 107^\circ
\]
**Step 4:**
Calculating the difference:
\[
x = 73^\circ
\]
Thus, the measure of the supplementary angle is \(73^\circ\).
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Simplify this solution Extra Insights
The measure of the supplementary angle can be found using the formula \( 180^{\circ} - \text{angle} \). So, for an angle measuring \( 107^{\circ} \), its supplementary angle would be \( 180^{\circ} - 107^{\circ} = 73^{\circ} \). Voilà! The supplementary angle measures \( 73^{\circ} \). Thinking of practical examples, supplementary angles often pop up in design and architecture. For instance, in creating stunning angular windows or intricate architectural features, knowing the supplementary angles can ensure all elements fit together harmoniously. Achieving that perfect balance in design often requires understanding and applying these basic geometric principles!
