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= °
We are given that the measure of the resulting angle, ∠1 + ∠2, is 135 degrees. Thus, we can set up the equation:
(2x) + (2x + 7) = 135
Simplifying, we have:
4x + 7 = 135
Subtracting 7 from both sides:
4x = 128
Dividing both sides by 4:
x = 32
Now we can substitute this value of x back into the expressions for ∠1 and ∠2 to find their measures:
m∠1 = 2x = 2(32) = 64 degrees
m∠2 = 2x + 7 = 2(32) + 7 = 71 degrees
Therefore, the two unknown angle measures are m∠1 = 64 degrees and m∠2 = 71 degrees.
Angle Pairs Unit Test
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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)
°
If the two angles are complementary, their measures add up to 90 degrees.
If one angle has a measure of 39 degrees, we can find the measure of the other angle by subtracting 39 from 90.
Therefore, the measure of the other angle is 90 - 39 = 51 degrees.
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° = °
Since the two angles are complementary, their measures add up to 90 degrees.
So, the equation for the angle measures can be written as:
(2x+3)° + 2x° = 90°
Angle Pairs Unit Test
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Question
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)°= °
To find the value of x and the two angle measures, we need to set up an equation using the fact that the two angles are complementary, meaning their measures add up to 90 degrees.
We have:
(2x)° + (3x)° = 90°
Combining like terms:
5x° = 90°
To solve for x, we divide both sides by 5:
x = 18
Now we can substitute this value into the expressions for the angle measures:
(2x)° = 2(18)° = 36°
(3x)° = 3(18)° = 54°
Therefore, x = 18, (2x)° = 36°, and (3x)° = 54°.