|
Question 998746: In quadrilateral MATH, angle M = x(degrees), angle A = 3x(degrees), angle T = (x-30)(degrees). What is the measure of an exterior angle at H, expressed in terms of x?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Let y = measure of the exterior angle at H
For any given interior angle, the exterior angle is simply 180 minus that given angle. For example, if the interior angle is 30 degrees, then the exterior angle is 180 - 30 = 150 degrees. If the interior angle is x degrees, then the exterior angle is 180 - x degrees.
angle M = x(degrees)
exterior to angle M = 180 - x
angle A = 3x(degrees)
exterior to angle A = 180 - 3x
angle T = (x-30)(degrees)
exterior to angle T = 180 - (x-30)
exterior to angle T = 180 - x+30
exterior to angle T = 210 - x
Summary so far:
exterior to angle M = 180 - x
exterior to angle A = 180 - 3x
exterior to angle T = 210 - x
exterior to angle H = y
In any polygon, the sum of the exterior angles is 360 degrees. This applies to quadrilaterals because they are 4 sided polygons.
(exterior angle for M)+(exterior angle for A)+(exterior angle for T)+(exterior angle for H) = 360
(180-x)+(180-3x)+(210-x)+(y) = 360
180-x+180-3x+210-x+y = 360
570-5x+y = 360
570-5x+y+5x = 360+5x
570+y = 360+5x
570+y-570 = 360+5x-570
y = -210+5x
y = 5x-210
At the top we said "Let y = measure of the exterior angle at H"
So because y = 5x-210, the exterior angle measure of H in terms of x is 5x-210
|
|
|
| |
