Question

May I please receive help

Answer 1

Answer:

y = 120°

z = 32°

Step-by-step explanation:

For the sake of simplicity, I labeled one of the interior angles as m < 1 (Please see the attached screenshot).  I did this because m < 1 and the exterior angle on the same side of the transversal have the same measure of m < 60°.  

Therefore,  m < 1 = m < 60°

Next, since m < 1 = 60°, then we can add its measure to < y°, which will sum up to 180° (given that they are supplementary angles).  

We can establish the following formula to solve for < y°:

       m < 1 + < y ° = 180°

Let's rearrange the formula to isolate < y°:

       < y ° = 180° - m < 1

Substitute the value of m < 1 into the revised formula:

      < y  = 180°- 60°

      < y = 120°

Now that we have the value for y°, we can find out what the value of z is by creating another formula:

        < (5z - 100)° = 180° -  y°

Substitute the value of y° into the formula:

5z - 100° = 180° - 120°

Combine like terms:

5z - 100° = 60°

Add 100° on both sides:

     5z - 100° + 100° = 60° + 100°

    5z = 160°

Divide both sides by 5:

    $\frac{5z}{5} = \frac{160}{5}$

    < z = 32°

Double-check whether we derived the correct answers by plugging in the values of y° and z° into the following formula:

y° + (5z - 100)° = 180°      (because they are supplementary angles)

120° + [5(32) - 100]° =  180°

120° + [5(32) - 100]° =  180°

120° + [160 - 100]° =  180°

120° + 60° = 180°

180° = 180°  (True statement).

Therefore, the value of y = 120° and z = 32°.  

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