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°
(5x-25)° + 55° = 180°
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?
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°.
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)°=
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°.
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
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.
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°
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°.