∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left bracket, 2, x, plus, 23, right bracket, degreesm∠1=(2x+23)
∘
and m, angle, 2, equals, left bracket, 4, x, plus, 25, right bracket, degreesm∠2=(4x+25)
∘
, then find the measure of angle, 2∠2.
Answer
Attempt 1 out of 2
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Since angles 1 and 2 are complementary, we have the equation:
m∠1 + m∠2 = 90 degrees
Substitute the expressions for m∠1 and m∠2:
(2x + 23) + (4x + 25) = 90
6x + 48 = 90
6x = 42
x = 7
Now, we can find the measure of angle 2:
m∠2 = 4x + 25
m∠2 = 4(7) + 25
m∠2 = 28 + 25
m∠2 = 53 degrees
Therefore, the measure of angle 2 (∠2) is 53 degrees.
∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left bracket, 6, x, plus, 18, right bracket, degreesm∠1=(6x+18)
∘
and m, angle, 2, equals, left bracket, 3, x, minus, 9, right bracket, degreesm∠2=(3x−9)
∘
, then find the measure of angle, 1∠1.
Answer
Attempt 1 out of 2
Since angles 1 and 2 are complementary, we have the equation:
m∠1 + m∠2 = 90 degrees
Substitute the expressions for m∠1 and m∠2:
(6x + 18) + (3x - 9) = 90
9x + 9 = 90
9x = 81
x = 9
Now, we can find the measure of angle 1:
m∠1 = 6x + 18
m∠1 = 6(9) + 18
m∠1 = 54 + 18
m∠1 = 72 degrees
Therefore, the measure of angle 1 (∠1) is 72 degrees.
∠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
Attempt 1 out of 2
Since angles 1 and 2 are complementary, we have the equation:
m∠1 + m∠2 = 90 degrees
Substitute the expressions for m∠1 and m∠2:
(x - 15) + (3x - 19) = 90
4x - 34 = 90
4x = 124
x = 31
Now, we can find the measure of angle 1:
m∠1 = x - 15
m∠1 = 31 - 15
m∠1 = 16 degrees
Therefore, the measure of angle 1 (∠1) is 16 degrees.
∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, 7, x, minus, 18, right bracket, degrees∠1=(7x−18)
∘
and mangle, 2, equals, left bracket, 6, x, minus, 8, right bracket, degrees∠2=(6x−8)
∘
, then find the measure of angle, 1∠1.
Answer
Attempt 1 out of 2
Vertical angles are congruent to each other, meaning they have the same measure.
Given that ∠1 and ∠2 are vertical angles, we have:
∠1 = ∠2
Now, set the expressions for ∠1 and ∠2 equal to each other:
7x - 18 = 6x - 8
x = 10
Now, substitute x back into the expression for ∠1 to find its measure:
∠1 = 7x - 18
∠1 = 7(10) - 18
∠1 = 70 - 18
∠1 = 52 degrees
Therefore, the measure of angle 1 (∠1) is 52 degrees.
∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 4, x, plus, 9, right bracket, degreesm∠1=(4x+9)
∘
and m, angle, 2, equals, left bracket, 3, x, minus, 4, right bracket, degreesm∠2=(3x−4)
∘
, then find the measure of angle, 2∠2.
Since angles 1 and 2 are supplementary, we have the equation:
m∠1 + m∠2 = 180 degrees
Substitute the expressions for m∠1 and m∠2:
(4x + 9) + (3x - 4) = 180
7x + 5 = 180
7x = 175
x = 25
Now, we can find the measure of angle 2:
m∠2 = 3x - 4
m∠2 = 3(25) - 4
m∠2 = 75 - 4
m∠2 = 71 degrees
Therefore, the measure of angle 2 (∠2) is 71 degrees.