Answer:
42. x = 25
43. LM = 11
Explanation:
For 42, the three angles of a triangle, when added, = 180 degrees. We know that one of the angles is 90 degrees...a right angle.
So: 90 + 2x + x + 15 = 180
105 + 3x = 180
3x = 75
x = 25
If they ask for more information: the three angles are 90 degrees, 50 degrees (2x), and 40 (x + 15). 90 + 50 + 40 = 180
For 43, ray PN bisects (cuts in equal halves) the triangle. We know this because the two segments LP and PM are equal. As a result, the triangles LPM and PNM are mirror images. Since MN = 11, LM also = 11.
Please let me know if you have questions.