Two adjacent angles, M<1 and M<2, form a resulting angle that measures 135 ° If M<1 = (2x) ° and m 2 = (2x + 7) what are the two unknown angle measures?
M<1 =
M<2 =
Choose two:
• 32
• 64
• 71
•158
To find the measures of M<1 and M<2, we can set up the following equation based on the given information:
M<1 + M<2 = 135
Substituting the given angle measures into the equation:
(2x) + (2x + 7) = 135
Combining like terms:
4x + 7 = 135
Subtracting 7 from both sides:
4x = 128
Dividing both sides by 4:
x = 32
Now we can find the measures of M<1 and M<2:
M<1 = (2x) = 2(32) = 64°
M<2 = (2x + 7) = 2(32) + 7 = 71°
Therefore, the unknown angle measures are M<1 = 64 and M<2 = 71.
An obtuse angle is formed by two adjacent angles with measures (x + 10) and (3x) ° If the resulting angle measure is 118° what is the angle measure of each of the two unknown angles? Round to the nearest whole number. (1 point)
• 43° and 75°
• 37° and 81°
• 20° and 98
• 34° and 84°
To find the angle measures of the two unknown angles, we can set up the following equation based on the given information:
(x + 10) + (3x) = 118
Combining like terms:
4x + 10 = 118
Subtracting 10 from both sides:
4x = 108
Dividing both sides by 4:
x = 27
Now we can find the angle measures of the two unknown angles:
First angle = (x + 10) = (27 + 10) = 37°
Second angle = (3x) = (3 * 27) = 81°
Therefore, the angle measures of the two unknown angles are 37° and 81°. So the correct answer is:
• 37° and 81°
For two vertical angles with measures m<1 = (4x + 26)° and m<3 = (3x + 32)° what is the measure of each angle? (1 point)
• 6
• 24
• 50
• 64
Vertical angles are formed by two intersecting lines and are always congruent. This means that the measure of angle 1 (m<1) is equal to the measure of angle 3 (m<3).
Therefore, we can set up the equation:
4x + 26 = 3x + 32
Subtracting 3x from both sides:
x + 26 = 32
Subtracting 26 from both sides:
x = 6
Now we can find the measure of each angle:
m<1 = 4x + 26 = 4(6) + 26 = 50°
m<3 = 3x + 32 = 3(6) + 32 = 50°
Therefore, the measure of each angle is 50°. So the correct answer is:
• 50
The m<2 = 47° Use this information and the information on the diagram to answer all of the following parts. There are 6 parts worth 1 point each.
a. Write an equation to solve for the m21
b. m< 4 =
c. m<5 =
a. Since angle 2 (m<2) is adjacent to angle 1 (m<1) and angle 2 (m<2) is vertical to angle 4 (m<4), we can write the equation:
m<1 + m<2 = m<4 + m<2
Substituting the given measure of angle 2 (m<2 = 47°) into the equation:
m<1 + 47° = m<4 + 47°
Therefore, the equation to solve for m<1 is:
m<1 = m<4
b. Since angles 1 (m<1) and 4 (m<4) are vertical angles, they have the same measure. Therefore,
m<4 = m<1
c. Since angle 4 (m<4) is opposite angle 5 (m<5) and vertical to angle 2 (m<2), we can write the equation:
m<2 = m<4 = m<5
Therefore:
m<5 = 47°