Problem

3) The figure shows several parking spaces at a mall. The parking spaces were created by drawing four parallel lines and a transversal. a. If $m \angle 1=111^{\circ}$, find $m \angle 4$. b. If $m \angle 2=(3 x-15)^{\circ}$ and $m \angle 3=(2 x-30)^{\circ}$, find the value of $x$

Solution

Step 1 :Given that $m \angle 1=111^{\circ}$, we know that when a transversal crosses parallel lines, alternate interior angles are congruent. Therefore, the measure of angle 4 should be equal to the measure of angle 1.

Step 2 :So, $m \angle 4 = \boxed{111^{\circ}}$.

Step 3 :Given that $m \angle 2=(3 x-15)^{\circ}$ and $m \angle 3=(2 x-30)^{\circ}$, we know that when a transversal crosses parallel lines, corresponding angles are congruent. Therefore, the measure of angle 2 should be equal to the measure of angle 3.

Step 4 :We can set up an equation and solve for x: $3x - 15 = 2x - 30$.

Step 5 :Solving the equation, we find that the value of $x$ is $\boxed{-15}$.

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Source: https://solvelyapp.com/problems/17414/

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