Here is one way...
These angles form a straight line, so they sum to 180° .
b + c + d = 180 Since c and d are vertical angles, c = d .
b + d + d = 180
b + 2d = 180
2d = 180 - b Divide through by 2 .
d = 90 - b/2
These angles form a straight line, so they sum to 180° .
a + d + (a - b) = 180 Since a and d are vertical angles, a = d .
d + d + (d - b) = 180
d + d + d - b = 180
3d - b = 180 Substitute 90 - b/2 in for d .
3(90 - b/2) - b = 180 Distribute the 3 .
270 - 3b/2 - b = 180 Subtract 270 from both sides.
-3b/2 - b = -90 Multiply through by 2 .
-3b - 2b = -180
-5b = -180 Divide both sides by -5 .
b = 36
Here is one way...
These angles form a straight line, so they sum to 180° .
b + c + d = 180 Since c and d are vertical angles, c = d .
b + d + d = 180
b + 2d = 180
2d = 180 - b Divide through by 2 .
d = 90 - b/2
These angles form a straight line, so they sum to 180° .
a + d + (a - b) = 180 Since a and d are vertical angles, a = d .
d + d + (d - b) = 180
d + d + d - b = 180
3d - b = 180 Substitute 90 - b/2 in for d .
3(90 - b/2) - b = 180 Distribute the 3 .
270 - 3b/2 - b = 180 Subtract 270 from both sides.
-3b/2 - b = -90 Multiply through by 2 .
-3b - 2b = -180
-5b = -180 Divide both sides by -5 .
b = 36
Thanks, hectictar...here's one more way...
Note that b and (a - b) are vretical angles so they equal each other
Therefore.... b = a - b → a = 2b
And c and d are vertical angles...so.... c = d
So we actually have this system
b + c + d = 180
a + d + (a - b) = 180 substituting, we have that
b + c + c = 180
2b + c + (2b - b) = 180 simplify
b + 2c = 180
3b + c = 180 multiply the second equation by -2
b + 2c = 180
-6b - 2c = -360 add these
-5b = -180 divide both sides by -5
b = 36