Find the measure of each angle.

Question

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.

Answer 1

Hello Ryan,

 

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