Question

Use the image to answer the question. Write an equation for the two adjacent angles.
(5x-25)° 55°

(2 points) (blank x− blank)° + blank° = blank°

Answer
Two adjacent angles form a resulting angle with measure 160°. m∠1=3x° and m∠2=(2x+10)°. Solve for x. What are the two unknown angles’ measurements?
Answer
Use the image to answer the question. An illustration shows three rays extending from a common origin. The angle measures between them are labeled. What are the two unknown angle measures that form the 90° angle? (1 point) (x+4)°= °, (3x+2)°=
Answer
For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x ?(1 point) Responses 30 30 60 60 20 20 15
Answer
A 180° angle (straight line) is formed by two adjacent angles. One angle has a measure of (2x+3)° and the other has a measure of (x−6)° . What are the measures of the two angles that make up the straight line?(1 point) Responses 129° and 51° 129 degrees and 51 degrees 121° and 59° 121 degrees and 59 degrees 125° and 55° 125 degrees and 55 degrees 186° and 88°
Answer
An obtuse angle is formed by two adjacent angles with measures (x−5)° and (3x)° . If the resulting angle measure is 107° , what is the angle measure of each of the two unknown angles? Round to the nearest whole number.(1 point) Responses 32° and 75° 32 degrees and 75 degrees 23° and 84° 23 degrees and 84 degrees 20° and 87° 20 degrees and 87 degrees 28° and 79°
Answered by GPT 3.5
(5x-25)° + 55° = 180°
Answered by GPT 3.5
We know that the sum of the measures of two adjacent angles is equal to the measure of the resulting angle.

So, we can write the equation:

3x + (2x + 10) = 160

Simplifying the equation:

5x + 10 = 160

Subtracting 10 from both sides:

5x = 150

Dividing both sides by 5:

x = 30

Now, we can substitute the value of x back into the expressions for the measures of angle 1 and angle 2:

m∠1 = 3x = 3(30) = 90°
m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70°

So, the measure of angle 1 is 90° and the measure of angle 2 is 70°.
Answered by GPT 3.5
Since we know that the sum of the interior angles of a triangle is always 180°, and we have two known angles of 90° and (x+4)°, we can write the equation:

90° + (x+4)° + (3x+2)° = 180°

Combining like terms:

4x + 96° = 180°

Subtracting 96° from both sides:

4x = 84°

Dividing both sides by 4:

x = 21°

Now, we can substitute the value of x back into the expressions for the unknown angle measures:

(x+4)° = (21+4)° = 25°
(3x+2)° = (3(21)+2)° = (63+2)° = 65°

Therefore, the two unknown angle measures are (x+4)° = 25° and (3x+2)° = 65°.
Answered by GPT 3.5
To find the value of x, we can set up the equation:

x + (x+30) = 90

Combining like terms:

2x + 30 = 90

Subtracting 30 from both sides:

2x = 60

Dividing both sides by 2:

x = 30

Therefore, x is equal to 30.
Answered by GPT 3.5
To find the measures of the two angles, we can set up the equation:

(2x+3) + (x-6) = 180

Combining like terms:

3x - 3 = 180

Adding 3 to both sides:

3x = 183

Dividing both sides by 3:

x = 61

Now we can substitute the value of x back into the expressions for the angles:

Angle 1 = (2x+3) = (2(61)+3) = 125°
Angle 2 = (x-6) = (61-6) = 55°

Therefore, the measures of the two angles that make up the straight line are 125° and 55°.
Answered by GPT 3.5
To find the angle measures, we can set up the equation:

(x-5) + (3x) = 107

Combining like terms:

4x - 5 = 107

Adding 5 to both sides:

4x = 112

Dividing both sides by 4:

x = 28

Now we can substitute the value of x back into the expressions for the angles:

Angle 1 = (x-5) = (28-5) = 23°
Angle 2 = (3x) = (3(28)) = 84°

Therefore, the angle measures of the two unknown angles are 23° and 84°.