|
Question 324732: Determine the measure (in degrees) of the third angle in an isosceles triangle, if the third angle is 10 more than one-half of either of the equal measure angles.
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! To solve this problem, you are going to have to write 2 equations using what you know.
First, you know that this is an isosceles triangle, meaning 2 of the angles are equal and all 3 angles add up to 180 degrees:
A + B + B = 180 or A + 2B =180 (with B = measure of either of the equal angles of the triangle in degrees, A = measure of the third angle in degrees)
Second, you know that the third angle (A) is 10 more than one-half of either of the equal measure angles (B):
A = 10 + (1/2)B
Now plug in the second equation into the first equation and solve for B:
A + 2B = 180
(10 + (1/2)B) + 2B = 180 (now add (1/2)B and 2B)
10 + (5/2)B = 180 (now subtract 10 from each side)
(5/2)B = 170 (now divide each side by (5/2), or 2.5 which is the same thing)
B = 68
So the measure of each of the equal angles is 68 degrees. Plug in this value to the first equation to find the measure of angle A:
A + 2B =180
A + (2*68) = 180
A + 136 = 180
A = 44
So the measure of the third angle in the triangle is 44 degrees.
|
|
|
| |
