Answer: [tex]C)62\°[/tex]
Step-by-step explanation:
The missing picture is attached.
And the missing options are:
[tex]A) 58\°\\ B)60\°\\ C)62\°\\ D)64\°[/tex]
For this exercise it is necessary to remember the definition of "Vertical angles".
Vertical angles are defined as those angles that are opposite to each other and share the same vertex. These angles are congruent, which means that they have equal measure.
You can identify in the picture that [tex]\angle XQL[/tex] and [tex]\angle MQR[/tex] are Vertical angles, then they are congruent.
Based on the above, you can set up the following equation:
[tex]-5b+82=-3b+74[/tex]
Now you must solve for "b" in order to find its value:
[tex]82-74=-3b+5b\\\\8=2b\\\\\frac{8}{2}=b\\\\b=4[/tex]
Finally, substituting the value of "b" into [tex]\angle XQL=-5b+82[/tex] and evaluating, you get:
[tex]\angle XQL=-5(4)+82\\\\\angle XQL=62\°[/tex]
