\( 2 x=30 \) b) If \( \angle 3=2 x+30 \) and \( \angle 5=3 x+100 \), find \( x \).

To solve for \( x \), first find \( x \) from the equation \( 2x = 30 \). Dividing both sides by 2 gives \( x = 15 \). Next, substitute \( x = 15 \) into the expressions for \( \angle 3 \) and \( \angle 5 \): - \( \angle 3 = 2(15) + 30 = 30 + 30 = 60^\circ \) - \( \angle 5 = 3(15) + 100 = 45 + 100 = 145^\circ \) Now that we have both angles, it's crucial to check whether they are related. If these angles are part of a linear pair, they should sum to \( 180^\circ \). Here, \( 60 + 145 = 205 \), which indicates they are not supplementary. Therefore, we’ve calculated correctly, but be sure to check the relationships between angles in geometry problems!