Question

I need help with 5-11

Answer 1

Step-by-step explanation:

5.

in an equilateral triangle all 3 sides are equally long. but that also means that all 3 angles are equal. and as the sum of all angles in a triangle has to be 180°, that means that each of the 3 Angie's is 180/3 = 60°.

so, KML = 60°.

6.

HMK = 50°, KML = 60°.

all angles around M on one side of the line LG must have 180° in total too.

so,

HMG = 180 - 50 - 60 = 70°

7.

since GHM is isoceles (GH and MH are equal), it means also that the angles at M and at G must be equal.

HMG = 70°

therefore, HGM = 70°

again, the sum of all angles in a triangle must be 180°, so

GHM = 180 - 70 - 70 = 40°.

8.

again, in an isoceles triangle also the 2 "bottom" angles are equal. and together with the 180 sum rule we get

MHJ = (180 - 145)/2 = 35/2 = 17.5°.

9.

if now the angle at G is 67°, then again, the angle at M must be equal (67°). and then again based on the 180 rule we get

GHM = 180 - 67 - 67 = 46°.

10.

since the 2 angles "at the bottom" are equal, it means ADE is an isoceles triangle.

since BC is parallel to DE, it means that ADE and ABC are similar triangles. and that means the corresponding angles are the same. and that means that the angles 3 and 4 are equal, and therefore ABC is an isoceles triangle. and that means that both legs AB and AC are equal.

11.

again, in an isoceles triangle the 2 base angles are equal. and together with the usual 180 rule that means

base angle = (180 - 18)/2 = 162/2 = 81°.