Answer:
[tex]m[/tex]∠[tex]B=71[/tex]°
Step-by-step explanation:
Complementary angles are a pair of angles whose measures have a sum of [tex]90[/tex]°. Therefore, [tex]m[/tex]∠[tex]A+m[/tex]∠[tex]B=90[/tex]°. We are given that [tex]m[/tex]∠[tex]A=2x+11[/tex] and [tex]m[/tex]∠[tex]B=17x+3[/tex]. Substituting these values into our equation gives us:
[tex]2x+11+17x+3=90[/tex]
Solving for [tex]x[/tex], we get:
[tex]2x+11+17x+3=90[/tex]
[tex]19x+14=90[/tex] (Simplify LHS)
[tex]19x+14-14=90-14[/tex] (Subtract [tex]14[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]19x=76[/tex] (Simplify)
[tex]\frac{19x}{19}=\frac{76}{19}[/tex] (Divide both sides of the equation by [tex]19[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=4[/tex] (Simplify)
Therefore, [tex]m[/tex]∠[tex]B=17x+3=17(4)+3=68+3=71[/tex]°. Hope this helps!
