## Monday, July 11, 2011

### Practice with angles of triangles and classification

Here are two earlier posts that have some practice problems with answers.

Look at Part B) in this post.

Look at problems 3) and 4) in this post.

Here are some more problems.

1)  You are told you have a right triangle.  If the second angle is given, either find the third angle or say it is not possible.
a) 84°
b) 31°
c) 102°

2) You are told you have an isosceles triangle.  If one angle less than 180° is given, there is always an isosceles triangle that has that measure as the size of one angle.  Sometimes, there is also a second possible triangle with that angle measure.  Find both triangles if possible, or find the only possible isosceles triangle with that angle measure and write NO SECOND TRIANGLE POSSIBLE as the second answer.

a) 84°
b) 31°
c) 102°

#### 1 comment:

Prof. Hubbard said...

1) You are told you have a right triangle. If the second angle is given, either find the third angle or say it is not possible.

a) 84°
The final angle is 6°, since 90°+84°+6° = 180°.

b) 31°
The final angle is 59°, since 90°+31°+59° = 180°.

c) 102°
A right triangle cannot also have an angle greater than 90°, so this one is NOT POSSIBLE.

2) You are told you have an isosceles triangle. If one angle less than 180° is given, there is always an isosceles triangle that has that measure as the size of one angle. Sometimes, there is also a second possible triangle with that angle measure. Find both triangles if possible, or find the only possible isosceles triangle with that angle measure and write NO SECOND TRIANGLE POSSIBLE as the second answer.

a) 84°
There could be two 84° angles, and since 180°-84°-84° = 12°, the three angles are 84°, 84° and 12°.

180°-84° = 96° and half of 96 is 48, so a second isosceles triangle is possible, 84°, 48° and 48°.

b) 31°
There could be two 31° angles, and since 180°-31°-31° = 118°, the three angles are 31°, 31° and 118°.

180°-31° = 149° and half of 149 is 74.5, so a second isosceles triangle is possible, 31°, 74.5° and 74.5°.

c) 102°

180°-102° = 78° and half of 78 is 39, so one isosceles triangle is possible, 102°, 39° and 39°.

There can't be two 102° angles, so a second isosceles triangle with a 102° angle is NOT POSSIBLE.