geometry triangle questions...?

Question

1. If the largest angle of an isosceles triangle measures 106°, find the measure of the smallest angle.

2. In a right triangle, if one acute angle has measure 6x - 10 and the other has measure 2x - 4 , find the larger of these two angles.

3. It is impossible for a triangle to be which of the following?

a. both isosceles and right
b. both equilateral and equiangular
c. both scalene and acute
d. both obtuse and equilateral

The first person to get all 3 correct first gets 10 points!! Thanks!

Answer 1

1. If the single largest angle is 106° that means that the smaller two angles are both (180° - 106°)/2 = 37°

2. (6x - 10)° + (2x - 4)° = 90°
   (8x - 14)° = 90°
   (8x)° = 104°
   (x)° = 13°

   the two angles, then, are (6*13 - 10)°
   and (2*13 - 4) or 68° and 22°

3. D. both obtuse and equilateral

Answer 2

1. The angles in a triangle add up to 180°. You have an isosceles triangle so it must have two equal angles. One angle is 106°, but you couldn't have two of them since that would exceed 180°. That means the remaining two angles must be the equal ones. Let's call that angle x.

106 + x + x = 180
2x = 74
x = 37

The smallest angle(s) are 37°

2. Add up the angles, solve for x
(6x - 10) + (2x - 4) + 90 = 180
(6x - 10) + (2x - 4) = 90
8x - 14 = 90
8x = 104
x = 13

Now the two angles are:
6x - 10
= 6(13) - 10
= 78 - 10
= 68

And:
2x - 4
= 2(13) - 4
= 26 - 4
= 22

The larger is 6x - 10 or 68°

3.
a. is possible (45-45-90)
b. is possible (60-60-60, the definition of an equilateral/equiangular triangle)
c. is possible (40-60-80, for example)
d. not possible. An equilateral triangle has all angles = 60° so none can be greater than 90° which is necessary for an obtuse triangle.

d. is the correct answer

Answer 3

1) 37 degrees (isosceles means 2 angles are equal)
2) 68 degrees (6x-10) + (2x-4) + 90 = 180
3) d (obtuse = angle > 90, equilateral = all angles are 60)

Answer 4

Do your homework sweetie. If you have any questions about the homework, then I might help...