A geometric figure has angles with the following measurements: 89° , 135° , 112° , 68° . Which two angle measures correspond to a supplementary pair? List the measure of the smaller angle first and the measure of the larger angle second.(1 point)
Smaller angle: °
Larger angle: °
The two angle measures that correspond to a supplementary pair are the ones that add up to 180°.
89° + 91° = 180°
So, the smaller angle is 89° and the larger angle is 91°.
Angles j and k are supplementary angles. What is m∠k if m∠j=34° ?(1 point)
°
Supplementary angles are two angles that add up to 180°.
Since m∠j = 34° and angles j and k are supplementary, we can set up the equation:
m∠j + m∠k = 180°
Substituting in the given value, we have:
34° + m∠k = 180°
To find m∠k, we can rearrange the equation:
m∠k = 180° - 34°
m∠k = 146°
Therefore, m∠k is 146°.
Use the image to answer the question.
An illustration shows a horizontal line with arrows at both ends. Another line with arrows at both ends extends from top right to bottom left and intersects the horizontal line in the center. The intersecting line creates 4 angles. The angle at the top left is labeled x degrees. The angle at top right is labeled y degrees. The angles at bottom left and right below the horizontal line are not labeled.
What is the value of x if y°=71° ?
(1 point)
°
Since the intersecting line creates a straight line with the horizontal line, angle x and angle y are supplementary angles.
Given that y° = 71°, we know that angle y has a measure of 71°.
Since angle x and angle y are supplementary, we can set up the equation:
x° + y° = 180°
Substituting in the given value for y°, we have:
x° + 71° = 180°
To find x°, we can rearrange the equation:
x° = 180° - 71°
x° = 109°
Therefore, the value of x is 109°.