Question Which theorems or postulates allow you to find the value of y? (1 point) Responses
Vertical Angles Theorem and Triangle Angle-Sum Theorem
Triangle Exterior Angles Theorem and Vertical Angles Theorem
Triangle Angle-Sum Theorem and Angle Addition Postulate
Angle Addition Postulate and Triangle Exterior Angles Theorem
The correct answer is: Triangle Angle-Sum Theorem and Angle Addition Postulate
The ratio of the angle measures of the acute angles in a right triangle is . What are the measures of these angles? (1 point) Responses
30° and 60°
45° and 90°
60° and 120°
10° and 20°
The correct answer is: 45° and 90°
The ratio of the angle measures of the acute angles in a right triangle is 1:2 What are the measures of these angles? (1 point) Responses
30° and 60°
45° and 90°
60° and 120°
10° and 20°
The correct answer is: 30° and 60°
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) Responses
30° and 40°
30° and 40°
54° and 72°
54° and 72°
60° and 80°
60° and 80°
77° and 103°
To find the measures of the other two angles, we can set up the equation:
3x + 4x + 40 = 180 (sum of angles in a triangle)
Combining like terms:
7x + 40 = 180
Subtracting 40 from both sides:
7x = 140
Dividing both sides by 7:
x = 20
Now, we can substitute x back into the equation to find the measures of the other two angles:
3x = 3(20) = 60°
4x = 4(20) = 80°
So, the measures of the other two angles are 60° and 80°. The correct answer is: 60° and 80°.