Finding Supplementary Angles in Leaf Veins
The question states that the veins in a leaf form a pair of supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees.
Given the measures of the two angles as \( m\angle1 = (7x + 13)^\circ \) and \( m\angle2 = (25x + 7)^\circ \), we can set up an equation that reflects their supplementary nature:
\[ (7x + 13) + (25x + 7) = 180 \]
Simplify the equation:
\[ 7x + 25x + 13 + 7 = 180 \]
\[ 32x + 20 = 180 \]
Now, solve for \( x \):
\[ 32x = 180 - 20 \]
\[ 32x = 160 \]
\[ x = \frac{160}{32} \]
\[ x = 5 \]
Now that we have the value of \( x \), we can find the measure of each angle:
\[ m\angle1 = 7x + 13 \]
\[ m\angle1 = 7(5) + 13 \]
\[ m\angle1 = 35 + 13 \]
\[ m\angle1 = 48^\circ \]
And for the other angle:
\[ m\angle2 = 25x + 7 \]
\[ m\angle2 = 25(5) + 7 \]
\[ m\angle2 = 125 + 7 \]
\[ m\angle2 = 132^\circ \]
So the measures of the two angles are 48 degrees and 132 degrees, respectively.
