The angle measures of triangle LMN are given: The measure of angle L is (5x−10)°.

 x = 10°

Step-by-step explanation:

Sum of all three angles of triangle = 180°

∠L + ∠M + ∠N = 180

5x -10 + 30 + 11x = 180        {Combine like terms}

5x +11x -10 + 30 =180

       16x  + 20   = 180   {subtract 20 from both sides}

                   16x = 180 - 20

                  16x = 160       {Divide both sides by 16}

              16x/16 = 160/16

                     x = 10°

x=9 i.e. option B is the answer.

Explanation:

Given that in triangle ABC, sides AB and BC are 36 and 28 units.

BD is angle bisector of angle B meeting AC at point D

Also AC = 16 cm.

We know that by angle bisector theorem,

AB/AC = BD/DC

Or x/DC = 36/28

By compendo and dividendo principle, we rewrite as

Or x/x+DC = 36/(28+36)

x/16 = 36/64

x = 36(16)/64 = 9 units.