The angles of a triangle are described as follows: A is the largest angle; its measure is twice the measure of B. The measure of C is 2 less than half the measure of B. Find the measures of the three angles in degrees.

Well, just remember that the total is

180

∘

for any triangle, ever. So, what we can construct are some simple relationships:

∠

A

=

∠

A

(1)

2

∠

B

=

∠

A

→

∠

B

=

∠

A

2

(2)

∠

C

=

∠

B

2

−

2

∘

→

∠

C

=

∠

A

4

−

2

∘

(3)

So, we can add them up to write and determine

∠

A

(and thus the other two):

∠

A

+

∠

B

+

∠

C

=

180

∘

∠

A

+

∠

A

2

+

∠

A

4

−

2

∘

=

180

∘

∠

A

+

∠

A

2

+

∠

A

4

=

182

∘

4

∠

A

4

+

2

∠

A

4

+

∠

A

4

=

182

∘

4

∠

A

+

2

∠

A

+

∠

A

=

728

∘

7

∠

A

=

728

∘

∠

A

=

104

∘

And of course, just plug things back into (2) and (3) to finish things up.

∠

B

=

52

∘

∠

C

=

24

∘

We can then verify that we've matched the conditions given.

∠

A

is indeed twice

∠

B

.

∠

C

is indeed

2

∘

less than half of

∠

B

. Finally, you can easily convince yourself that the three angles add up to

180

∘

.