∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, 3, x, plus, 22, right bracket, degrees∠1=(3x+22)

Question

∘
and mangle, 2, equals, left bracket, 7, x, minus, 22, right bracket, degrees∠2=(7x−22)
∘
, then find the value of x.

Answer 1

Since ∠1 and ∠2 are vertical angles, they are equal in measure. Therefore, we can set up the equation:

3x + 22 = 7x - 22

Now, we can solve for x:

4x = 44
x = 11

Therefore, the value of x is 11.

Answer 2

∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 4, x, minus, 23, right bracket, degreesm∠1=(4x−23)
∘
and m, angle, 2, equals, left bracket, 2, x, plus, 11, right bracket, degreesm∠2=(2x+11)
∘
, then find the measure of angle, 1∠1.

Answer 3

Since ∠1 and ∠2 are supplementary angles, their measures add up to 180 degrees. Therefore, we can set up the equation:

(4x - 23) + (2x + 11) = 180

Now, we can solve for x:

6x - 12 = 180
6x = 192
x = 32

Now, we can substitute x back into the expression for ∠1 to find its measure:

∠1 = 4x - 23
∠1 = 4(32) - 23
∠1 = 128 - 23
∠1 = 105 degrees

Therefore, the measure of angle ∠1 is 105 degrees.

Answer 4

∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left bracket, x, plus, 2, right bracket, degreesm∠1=(x+2)
∘
and m, angle, 2, equals, left bracket, x, minus, 26, right bracket, degreesm∠2=(x−26)
∘
, then find the measure of angle, 1∠1.

Answer 5

Since ∠1 and ∠2 are complementary angles, their measures add up to 90 degrees. Therefore, we can set up the equation:

(x + 2) + (x - 26) = 90

Now, we can solve for x:

2x - 24 = 90
2x = 114
x = 57

Now, we can substitute x back into the expression for ∠1 to find its measure:

∠1 = x + 2
∠1 = 57 + 2
∠1 = 59 degrees

Therefore, the measure of angle ∠1 is 59 degrees.

Answer 6

∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left bracket, x, minus, 15, right bracket, degreesm∠1=(x−15)
∘
and m, angle, 2, equals, left bracket, 3, x, minus, 19, right bracket, degreesm∠2=(3x−19)
∘
, then find the measure of angle, 1∠1.

Answer 7

Since ∠1 and ∠2 are complementary angles, their measures add up to 90 degrees. Therefore, we can set up the equation:

(x - 15) + (3x - 19) = 90

Now, we can solve for x:

4x - 34 = 90
4x = 124
x = 31

Now, we can substitute x back into the expression for ∠1 to find its measure:

∠1 = x - 15
∠1 = 31 - 15
∠1 = 16 degrees

Therefore, the measure of angle ∠1 is 16 degrees.

Answer 8

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, 4, x, plus, 6, right bracket, degrees∠1=(4x+6)
∘
and mangle, 2, equals, left bracket, 2, x, plus, 18, right bracket, degrees∠2=(2x+18)
∘
, then find the value of x.

Answer 9

Since ∠1 and ∠2 are vertical angles, they are equal in measure. Therefore, we can set up the equation:

4x + 6 = 2x + 18

Now, we can solve for x:

4x - 2x = 18 - 6
2x = 12
x = 6

Therefore, the value of x is 6.

Answer 10

Solve for the value of n.
(3n-5)°
(2n)°

Answer 11

To solve for n, we set the two expressions equal to each other since they are vertical angles:

3n - 5 = 2n

Now, solve for n:

3n - 2n = 5
n = 5

Therefore, the value of n is 5.