as you can see, there are three right angles
first find the measure of angle
then we know that the sum of
third angle in second right triangle is
so,
since angle
Let A be the vertex at angle "a";
B be the vertex at angle "b",
C be the vertex at angle "c",
D be the vertex at angle 37°,
P be the intersection point of the two sloped lines.
From triangle ABC, we can write equation
angle(A) + angle(B) + angle(C) = 180°
or
2a + (180°-2b) + c = 180°
or
2a - 2b + c = 0. (1)
Next consider triangles APC and BPD. From these triangles, we can write equation
a + c = b + 37°.
It is because left side (a+c) complements angle P to 180°,
same as right side (b+37°) complements angle P to 180°.
Last equation is equivalent to
a - b + c = 37°. (2)
Thus we have two equations (1) and (2)
2a - 2b + c = 0. (1)
a - b + c = 37°. (2)
Multiply equation (2) by 2; then subtract equation (1). You will get
c = 2*37° = 74°.
ANSWER. The measure of angle "c" is 74°.
bo = a + 37o ----- External angle = sum of interior opposite angles b + b = 2(a + 37) 2b = 2a + 74 2b = 2a + c ----- External angle = sum of interior opposite angles Therefore, 2a + 74 = 2a + c 2a + 74 - 2a = c 74o = c