There is a point M inside a square ABCD such that angle MAB is 60° and angle MCD is 15°. Find angle MBC.

Drawing out the square, call angle AMB x, angle MBA z, and angle BMC y

The 3 angles in a triangle add up to 180.... so:

x + z + 60 = 180
so x + z = 120

(90-z) + 75 + y = 180
so y - z = 15

Since z = 120 - x
y - (120 - x) = 15
so y + x = 135

Solve:
x + z = 120
y - z = 15
y + x = 135
Knowing that x, y, z are all >0 and <90

x = 60, y = 75, and z = 60

Angle MBC is 90 - z = 30

 

Posted by Telly on 2004-06-11 10:42:54