Use the image to answer the question.
An illustration shows four rays with points near the arrows labeled A, B, C, and D in a clockwise direction emerging from a common point labeled O. The angle A O B is marked as 40 degrees and angle C O D is marked as 50 degrees.
Are the two indicated angles adjacent? Why or why not?
(1 point)
Responses
No, the two indicated angles do not share a common vertex.
No, the two indicated angles do not share a common vertex.
No, the two indicated angles do not share a common ray.
No, the two indicated angles do not share a common ray.
Yes, the two indicated angles share a common vertex.
Yes, the two indicated angles share a common vertex.
Yes, the two indicated angles share a common ray.
No, the two indicated angles do not share a common ray.
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)
To find the measure of angle TSV, we need to add the measures of angles TSR and VSR, which are angles that share a common side with angle TSV.
Angle TSR = Angle TSR = 157 degrees
Angle VSR = Angle VSR = 54 degrees
Therefore,
∠TSV = ∠TSR + ∠RSV
= 157 + 54
= 211 degrees
So, the measure of angle TSV is 211 degrees.
Two adjacent angles, ∠1
and ∠2
, form a resulting angle with measure 135° . If m∠1=(2x)° and m∠2=(2x+7)° , what are the two unknown angle measures?(1 point)
m∠1=
°, m∠2=
°
Let's set up an equation based on the information given:
m∠1 + m∠2 = 135
Given:
m∠1 = (2x)°
m∠2 = (2x + 7)°
Substitute these values into the equation:
(2x) + (2x + 7) = 135
4x + 7 = 135
4x = 135 - 7
4x = 128
x = 128 / 4
x = 32
Now, substitute x back into the expressions for m∠1 and m∠2:
m∠1 = (2 * 32) = 64°
m∠2 = (2 * 32 + 7) = 71°
Therefore, the measures of the two unknown angles are:
m∠1 = 64°
m∠2 = 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)
°
Since the angles are complementary, we know that their measures add up to 90 degrees.
If one angle has a measure of 39 degrees, then the measure of the other angle can be found by subtracting 39 degrees from 90 degrees.
90 - 39 = 51
Therefore, the measure of the other angle is 51 degrees.
A figure shows two nonadjacent angles with measures (2x+3)° and 2x° . If the angles are complementary, what is the equation for the angle measures?(1 point)
(
)° + 2x° =
°
Since the angles are complementary, their measures add up to 90 degrees.
The measures of the angles are (2x+3)° and 2x°, so the equation for their measures, when added together, equals 90 degrees is:
(2x+3) + 2x = 90
Simplify the equation:
4x + 3 = 90
Therefore, the equation for the angle measures is: (4x + 3)° + 2x° = 90°
Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)
x=
, (2x)°=
°, and (3x)°=
°