The measures of two supplementary angles, and , are in the ratio of 3:7, respectively.
What is the value of ?

Ask by Campos Cole. in the United Arab Emirates

Jan 11,2025

Question

The measures of two supplementary angles, $$ m^{\circ} $$ and $$ n^{\circ} $$, are in the ratio of 3:7, respectively. What is the value of $$ n $$ ?

UpStudy AI · Accepted Answer

Two angles are supplementary if they add up to $$ 180^\circ $$. Let's denote the measures of the two angles as $$ 3x $$ and $$ 7x $$ based on the given ratio of $$ 3:7 $$.

1. **Set Up the Equation:**
   
   $$
   3x + 7x = 180
   $$

2. **Combine Like Terms:**
   
   $$
   10x = 180
   $$

3. **Solve for $$ x $$:**
   
   $$
   x = \frac{180}{10} = 18
   $$

4. **Find the Measure of Angle $$ n $$:**
   
   Since $$ n = 7x $$:
   
   $$
   n = 7 \times 18 = 126^\circ
   $$

**Answer:** $$ n = 126^\circ $$
$$ n = 126^\circ $$

The measures of two supplementary angles, and , are in the ratio of 3:7, respectively.
What is the value of ?

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The measures of two supplementary angles, and , are in the ratio of 3:7, respectively. What is the value of ?