Answer:
h=55
Step-by-step explanation:
1. Determine that the two unknown interior angles of the triangle are congruent. This is true because they are both equal to (180-2h) degrees. You know this because straight lines at to 180 degrees, so (2h) degrees plus the unkown angle is 180 degrees.
2. Solve for triangle's interior angles. Triangles' angles add up to 180 degrees, and you are given that one angle is 40 degrees and you just determined that the other two angles are congruent. Set up the equation 180=40+2x, in which x=the degrees in each of the unkown angles.
2x+40=180, 2x=140, x=70. Each of the unknown interior angles is 70 degrees.
3. Use the straight angle theorem to solve for h. In step 1, we determined that the interior angles were each equal to 180-2h, so the equation was x=180-2h. You know know x, so plug it in and solve for h.
180-2h=70
-2h=-110
2h=110
h=55
