Question

The measure of one angle of a triangle is 40°. The measures of the other two angles are in a ratio of 3:4. What are the measures of these two angles? (1 point)

30° and 40°
54° and 72°
60° and 80°
77° and 103°

Answer 1

1.
Let the measures of the triangle be 40°, a and b.

2.
a and b are in the ratio 3:4, so let a=3t and b=4t.

(check: a:b = 3t: 4t = 3:4)

3.
So the measures of the angles are 40°, 3t and 4t.

4.
the sum of the measures of the interior angles of any triangle is 180°,

thus :

40° + 3t + 4t =180°

40°+7t=180°

7t=180°-40°

7t=140°

t=140°/7=20°

5.
thus the measures of the angles are:

a=3t=3*20°=60°

and

b=4t=4*20°=80°.


Answer: 60° and 80°

Answer 2

For a triangle.
40+3x+4x=180
The other two angles are 60 degrees and 80 degrees.