Use the image to answer the question.
An illustration shows three rays passing through three points from a common origin point at upper S. Point upper T is to the horizontal left of upper S. A ray from upper S joins upper T with an arrow near upper T. Point upper V is on the top inclined to the right of point upper S. A ray from upper S joins upper V with an arrow near upper V. Point upper R is to top right of point upper S, below point upper V. A ray from upper S joins upper R with an arrow near upper R. Angle upper T upper S upper R is labeled as 157 degrees. Angle upper V upper S upper R as 54 degrees.
What is the measure of ∠TSV?
(1 point)
∠TSV = 29 degrees.
Use the image to answer the question.
An illustration shows three rays from a common vertex with labeled angles. The first ray is inclined to the horizontal left of the common vertex with an arrow at the end. The second ray is inclined to the horizontal right of the common vertex with an arrow at the end. The third ray is to the top right of the common vertex with an arrow at the end. It is between the other two rays. The angle between the first and the third rays is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. The angle between the second and third rays is labeled as left parenthesis x minus 6 right parenthesis degrees.
What is an equation for these two adjacent angles?
(2 points)
(2x + 3) + (x - 6) = 3x - 3
Two adjacent angles form a resulting angle of 135°. ∠1=(2x)° and ∠2=(2x+7)°. What are the two unknown angles?(1 point)
We know that:
∠1 + ∠2 = resulting angle
Substituting the given values:
(2x)° + (2x + 7)° = 135°
Simplifying the equation:
4x + 7 = 135
4x = 128
x = 32
Substituting x = 32 in the expressions for the angles:
∠1 = (2x)° = 64°
∠2 = (2x + 7)° = 71°
Therefore, ∠1 is 64° and ∠2 is 71°.
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39 , what is the other angle measure?(1 point)
Two angles are complementary if their sum is equal to 90 degrees.
Let's denote the measure of the other angle as x.
Since the angles are complementary:
x + 39 = 90
Subtracting 39 from both sides:
x = 51
Therefore, the measure of the other angle is 51 degrees.
A figure shows two nonadjacent angles (2x+3)° and 2x°. If the angles are complementary, what is the equation for the angles?(1 point)
Since the two angles are complementary, their sum is 90 degrees.
So we have the equation:
(2x + 3)° + 2x° = 90°
Simplifying the equation:
4x + 3 = 90
4x = 87
x = 21.75
Therefore, the two angles are:
(2x + 3)° = (2(21.75) + 3)° = 46.5°
2x° = 2(21.75)° = 43.5°
So the equation for the angles is:
46.5° + 43.5° = 90°
A figure shows two nonadjacent angles (2x+3)° and 2x°. If the angles are complementary, what is the equation for the angles?(1 point)
+ 2x° = °