Given that m∠1 = (2x)° and m∠2 = (2x+7)°, we know that the sum of the two angles is equal to 135°.
So, (2x)° + (2x+7)° = 135°
Combining like terms, we have 4x + 7 = 135.
Subtracting 7 from both sides, we get 4x = 128.
Dividing both sides by 4, we have x = 32.
Therefore, m∠1 = (2(32))° = 64°, and m∠2 = (2(32)+7)° = 71°.
So, the two unknown angle measures are m∠1 = 64° and m∠2 = 71°.
Two adjacent angles, ∠1
and ∠2
, form a resulting angle with measure 135°. If m∠1=(2x)° and m∠2=(2x+7)°, what are the two unknown angle measures?(1 point)
m∠1=
°, m∠2=
°
11 answers
Angle Pairs Unit Test
5 of 155 of 15 Items
Question
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39° , what is the other angle measure?(1 point)
°
5 of 155 of 15 Items
Question
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39° , what is the other angle measure?(1 point)
°
Complementary angles are two angles whose measures add up to 90°.
Given that one of the angles has a measure of 39°, we can subtract this measure from 90° to find the measure of the other angle.
90° - 39° = 51°
Therefore, the measure of the other angle is 51°.
Given that one of the angles has a measure of 39°, we can subtract this measure from 90° to find the measure of the other angle.
90° - 39° = 51°
Therefore, the measure of the other angle is 51°.
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)
(
)° + 2x° =
°
(
)° + 2x° =
°
Given that the angles are complementary, the sum of their measures is 90°.
So, (2x+3)° + 2x° = 90°.
Combining like terms, we have 4x + 3 = 90.
Subtracting 3 from both sides, we get 4x = 87.
Dividing both sides by 4, we have x = 21.75.
Therefore, the equation for the angle measures is (2(21.75) + 3)° + 2(21.75)° = 90°.
Simplifying, we have (43.5 + 3)° + 43.5° = 90°.
Which gives us 46.5° + 43.5° = 90°.
So, the equation for the angle measures is 46.5° + 43.5° = 90°.
So, (2x+3)° + 2x° = 90°.
Combining like terms, we have 4x + 3 = 90.
Subtracting 3 from both sides, we get 4x = 87.
Dividing both sides by 4, we have x = 21.75.
Therefore, the equation for the angle measures is (2(21.75) + 3)° + 2(21.75)° = 90°.
Simplifying, we have (43.5 + 3)° + 43.5° = 90°.
Which gives us 46.5° + 43.5° = 90°.
So, the equation for the angle measures is 46.5° + 43.5° = 90°.
Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)
x=
, (2x)°=
°, and (3x)°=
°
x=
, (2x)°=
°, and (3x)°=
°
Complementary angles have measures that add up to 90°.
Given that the measures of the angles are (2x)° and (3x)°, we can set up the equation:
(2x)° + (3x)° = 90°
Combining like terms, we have 5x = 90.
Dividing both sides by 5, we get x = 18.
Therefore, x = 18, and substituting x into the angle measures, we have:
(2(18))° = 36°, and (3(18))° = 54°.
So, x = 18, (2x)° = 36°, and (3x)° = 54°.
Given that the measures of the angles are (2x)° and (3x)°, we can set up the equation:
(2x)° + (3x)° = 90°
Combining like terms, we have 5x = 90.
Dividing both sides by 5, we get x = 18.
Therefore, x = 18, and substituting x into the angle measures, we have:
(2(18))° = 36°, and (3(18))° = 54°.
So, x = 18, (2x)° = 36°, and (3x)° = 54°.
Angles j and k are supplementary angles. What is m∠j if m∠k=117° ?(1 point)
°
°
Supplementary angles are two angles whose measures add up to 180°.
Given that m∠k = 117°, we can subtract this measure from 180° to find the measure of m∠j.
180° - 117° = 63°
Therefore, m∠j = 63°.
Given that m∠k = 117°, we can subtract this measure from 180° to find the measure of m∠j.
180° - 117° = 63°
Therefore, m∠j = 63°.
Two supplementary angles have measures m∠ABC=105° and m∠CBD=(3x−24)° . What is the equation to solve for x ? (1 point)
(3x−24)°+
°=
°
(3x−24)°+
°=
°
Supplementary angles have measures that add up to 180°.
Given that m∠ABC = 105° and m∠CBD = (3x - 24)°, we can set up the equation:
105° + (3x - 24)° = 180°
Combining like terms, we have 3x - 24 + 105 = 180°
Simplifying further, we get 3x + 81 = 180°
Subtracting 81 from both sides, we have 3x = 99°
Dividing both sides by 3, we get x = 33°
Therefore, the equation to solve for x is (3x - 24)° + 105° = 180°, which simplifies to 3x - 24 + 105 = 180°.
Given that m∠ABC = 105° and m∠CBD = (3x - 24)°, we can set up the equation:
105° + (3x - 24)° = 180°
Combining like terms, we have 3x - 24 + 105 = 180°
Simplifying further, we get 3x + 81 = 180°
Subtracting 81 from both sides, we have 3x = 99°
Dividing both sides by 3, we get x = 33°
Therefore, the equation to solve for x is (3x - 24)° + 105° = 180°, which simplifies to 3x - 24 + 105 = 180°.