Explanation:
let's start with the isoceles triangle with 36°.
remember, the sum of all angles in a triangle is always 180°. and the base angles of an isoceles triangle are equal.
so,
180 = 36 + 2×a
144 = 2a
a = 72°
g is then the complementary angle to the second a angle (it means they have together 90°) :
90 = g + a = g + 72
g = 18°
h is per the rules of equal angles on both sides of intersected lines the same as the second a angle, as it is also complementary to the g angle :
h = a = 72°
m is the supplementary angle (that means together they have 180°) to g, as the invective angle next to m is the same as g, due to the rules of equal angles of intersected parallel lines. and the sum of all angles around a point on one side of a line must be 180°.
180 = m + g = m + 18
m = 162°
in the upper triangle with o and n we have the baseline being 2 times the height, and it is therefore an isoceles triangle.
both sides are congruent isoceles triangles.
both baseline angles are therefore o and respectively n.
making o = n.
and so, for the complete upper triangle we have the angles o, o and 2o (or n, n and 2n).
180 = o + o + 2o = 4o
o = 180/4 = 45° = n
the f and o triangle is a triangle of 90°, f and o.
180 = 90 + f + o = 90 + f + 45
f = 45°
e + f + 298 = 360
because together they represent a full circle
e = 360 - 298 - f = 62 - 45 = 17°
in the o and b triangle we have a third angle (90 + g). and therefore
180 = o + b + 90 + g = 45 + b + 90 + 18
b = 180 - 90 - 45 - 18 = 27°
k is again per the rules of the same angles on both sides of intersecting lines (incl. parallel lines) the same as n :
k = n = 45°
for the same reason p = j = d
and p is the supplementary angle to k (again, parallel lines intersect another line with the same angles).
180 = k + p = 45 + p
p = j = d = 180 - 45 = 135°
i is the same as the unnamed third angle in the h and n triangle.
180 = h + n + i = 72 + 45 + i
i = 180 - 72 - 45 = 63°
c is the supplementary angle to (e + f). again, due to the same angles on both sides of intercepted lines (and of course, also parallel intercepted lines).
180 = e + f + c = 17 + 45 + c
c = 180 - 17 - 45 = 118°
the unnamed smaller angle next to c is equal to n (again, same intersection angles for parallel lines). so the larger unnamed angle next to c is then the supplementary angle to n, therefore the same as p, j and d : 135°.
now, to get l we need to remember that the sum of all angles in any quadrilateral is 360°.
our quadrilateral is here these unnamed 135°, l, c and e.
so,
360 = 135 + l + 118 + 17
l = 360 - 135 - 118 - 17 = 90°