Question - Finding Supplementary Angles in Leaf Veins
Solution:
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.
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