Answer:
1. x = 80°
2. x = 95°
3. x = -7
4. x = 32°
5. Yes, it is possible
Explanation:
For questions 1, 2 and 3 we make use of the fact that the sum of the angles of a triangle = 180
Q1
Angle measures are 60, 40 and x
So 60 + 40 + x = 180
==> 100 + x = 180
==> x = 180 - 100 = 80°
Q2
Angles are 35, 50 and x
35 + 50 + x = 180
85 + x = 180
x = 180 - 85 = 95°
Q3
Angle measures are
76, 41 and (x + 70)
76 + 41 + x + 70 = 180
187 + x = 180
x = 180 - 187
x = -7
Note: x is not an angle of the triangle, 70 + x is the third angle measure and that = 70 - 7 = 63°
Q4:
One leg of the triangle is extended creating an exterior angle of 122°
When an exterior angle is formed in this manner, it is equal to the sum of the two interior angles
The two interior angle measures are x° and 90°
So x + 90 = 122
x = 122-90 = 32°
Q5
One property of any triangle is that the sum of the lengths of any two sides must be greater than the length of the third side
Given three sides 85, 45, 45
45 + 45 = 90 > 85
45 + 85 = 130 > 45
So it is possible to have a triangle with lengths 85, 45 and 45