Answer:
15) m∠A = 21°, m∠B = 125°, m∠C = 34°
16) m∠J = 48°, m∠K = 57°, m∠L = 75°
Explanation:
15) m∠A is thirteen less than m∠C, so if you were to translate that into numerical terms, it would be (x-13). m∠B is eleven less than four times m∠C, so that would be (4x-11). Because the angles of a triangle sum up to 180°, the equation for this scenario would be (x-13)+(4x-11)+x=180. (X is a variable for m∠C. Add all the like terms to get 6x-24=180. Add 24 to both sides to get 6x=204. Divide 6 on both sides to get x=34. Now that we know m∠C, we can substitute 34 into x to get m∠A as 21° and m∠B as 125°.
16) m∠K is 9 more than m∠J, which is (x+9). m∠L is 21 less than twice m∠J, which is (2x-21). Again, a triangle's angles sum up to 180°, so the equation would be (x+9)+(2x-21)+x=180. Add the like terms to get 4x+(-12)=180. Add 12 to both sides to get 4x=192. Divide 4 on both sides to get x=48. Substitute 48 for x to get m∠K = 57° and m∠L=75°.