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)

Question

(__)° + 2x° = __°

Answer 1

In a complementary angle relationship, the sum of the angles is equal to 90 degrees.

So, the equation for the angle measures is:
(2x+3)° + 2x° = 90°

Answer 2

Two complementary angles have measures (2x)° and (3x)°. What is the value of x and the two angle measures?

x = __, (2x)° = __°, and (3x)° = __°

Answer 3

In a complementary angle relationship, the sum of the angles is equal to 90 degrees.

So, we can set up the equation:

(2x)° + (3x)° = 90°

Combining like terms, we have:

5x° = 90°

To solve for x, we divide both sides of the equation by 5:

5x/5 = 90/5
x = 18

Now that we have the value of x, we can substitute it back into the equations to find the angle measures:

(2x)° = 2 * 18° = 36°
(3x)° = 3 * 18° = 54°

Therefore, x = 18, (2x)° = 36°, and (3x)° = 54°.

Answer 4

Angles j and k are supplementary angles. What is  m∠j  if  m∠k=117° ?

__°

Answer 5

When two angles are supplementary, their sum is 180 degrees.

So, if m∠k = 117°, then:

m∠j + m∠k = 180°

Substituting in the known value:

m∠j + 117° = 180°

To solve for m∠j, we can subtract 117° from both sides:

m∠j = 180° - 117°
m∠j = 63°

Therefore, m∠j is 63°.

Answer 6

Two supplementary angles have measures  m∠ABC=105° and m∠CBD=(3x−24)° . What is the equation to solve for x ?
(3x - 24)° +__° = __°

Answer 7

If two angles are supplementary, their sum is 180 degrees.

So, we can set up the equation:

m∠ABC + m∠CBD = 180°

Substituting the known values:

105° + (3x - 24)° = 180°

To solve for x, we can subtract 105° from both sides:

3x - 24° = 180° - 105°
3x - 24° = 75°

To isolate x, we can then add 24° to both sides:

3x = 75° + 24°
3x = 99°

Finally, to solve for x, we divide both sides by 3:

x = 99° / 3
x = 33°

To find the equation,

(3x - 24)° + __° = __°

we substitute the value of x:

(3*33 - 24)° + __° = __°
(99 - 24)° + __° = __°
75° + __° = __°

Therefore, the equation to solve for x is (3x - 24)° + 75° = __°.

Answer 8

fill in the last blank

Answer 9

The equation to solve for x is (3x - 24)° + 75° = __°.

To fill in the last blank, we can simplify the equation:

(3x - 24)° + 75° = __°
3x + 51° = __°

Therefore, the equation to solve for x is (3x - 24)° + 75° = 3x + 51°.

Answer 10

Two angles are supplementary with measures  m∠ACB=4x° and m∠BCD=(6x+50)° . What is the measure of ∠ACB ?

m∠ACB = __°

Answer 11

If two angles are supplementary, their sum is 180 degrees.

So, we can set up the equation:

m∠ACB + m∠BCD = 180°

Substituting the given angle measures:

4x° + (6x + 50)° = 180°

To solve for x, we can combine like terms and isolate it:

10x + 50° = 180°

Subtracting 50° from both sides:

10x = 180° - 50°
10x = 130°

Finally, dividing both sides by 10:

x = 130° / 10
x = 13°

Therefore, the measure of ∠ACB is:

m∠ACB = 4x° = 4 * 13° = 52°