Find the measure of the requested angle.
(E and D are the requested angles.)
(The angles are a total of 6 from three intersecting lines, and the requested angles are the two at the bottom. One angle at the top is 31, while one side angle is 86.)
To find the measure of the requested angles, E and D, we can use the property that when two lines intersect, opposite angles are equal.
Since the angle at the top is 31 degrees, the angle opposite it is also 31 degrees. Therefore, angle E + 31 = 180 degrees (since they form a straight line). So angle E = 180 - 31 = 149 degrees.
Similarly, since the side angle is 86 degrees, the angle opposite it is also 86 degrees. Therefore, angle D + 86 = 180 degrees. So angle D = 180 - 86 = 94 degrees.
Therefore, the measure of angle E is 149 degrees and the measure of angle D is 94 degrees.
Angle D and 31 are congruent, however E and 86 are not.
Apologies for the error. Let's correct that:
Since the angle at the top is 31 degrees, the angle opposite it (angle D) is also 31 degrees.
Therefore, angle D = 31 degrees.
Now, to find angle E, we know that the total sum of angles at the intersection point is 180 degrees.
31 degrees (angle D) + 86 degrees (side angle) + angle E = 180 degrees
Substitute the values:
31 + 86 + angle E = 180
117 + angle E = 180
angle E = 180 - 117
angle E = 63 degrees
Therefore, the measure of angle D is 31 degrees and the measure of angle E is 63 degrees.
oh, it was my own error, apologies.
Angle E and 31 are congruent.
The angle that is 86 is congruent to its other side. And the angle above angle D is congruent to it.
The only angle we are missing now is Angle D.
No problem at all. Let's find the measure of angle D:
Since the angle at the top is 31 degrees, the angle opposite it (angle E) is also 31 degrees.
Therefore, angle E = 31 degrees.
The side angle is 86 degrees, which means the angle opposite it (angle D) is also 86 degrees.
Therefore, angle D = 86 degrees.
Therefore, the measure of angle D is 86 degrees.