The measure of the first angle of a triangle is 3° more than the measure of the second angle. The measure of the third angel is 5° more than twice the measure of the second angle. Find the measure of each angle.
Find the measure of each angle.
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Essentially this is a word problem so you need to read carefully. Start by labeling each angle. Call angle 1 A, 2 is B and 3 is C, pretty standard for triangles.
sentence 1 says that A = 3°+B
Sentence 2 says that C = 5° + 2B
And we know that angle B = B
Another important known is that for a triangle of any type, right, obtuse, ... the sum of the 3 angles is 180°
Now just add the 3 angles together:
A + B + C = 180°, simplify
3°+B + B + 5° + 2B = 180°, simplify
8°+4B = 180°, Now solve for B
4B = 172°
B = 43°, now backfill the value of B into our sentences above
A = 3°+B = 3°+43° = 46°
C = 5° + 2B = 5° + 2(43°) = 5° + 86° = 91°
A = first angle = 46°
B = second angle = 43°
C = third angle = 91°, This means that your triangle is an obtuse triangle with an angle greater than 180°
Hope that helps, good luck