In triangle PQR,A and B are midpoints of segment PQ and segment RQ,respectively.If PR=16,measure of angle P is 58 degrees, and measure of angle Q is 38 degrees, what is measure of angle ABR?
angle R = 180-58-38 = 84°
Now you can use the fact that AB║PR to use corresponding angles and their supplements to find the other two angles of the trapezoid.
96 degrees?
That's what I get.
To find the measure of angle ABR in triangle PQR, we can use the concept of the Midsegment Theorem.
The Midsegment Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. Additionally, it divides the third side into two equal segments.
In this case, A and B are the midpoints of PQ and RQ, respectively. Therefore, line AB is parallel to PR and half its length. Since PR is 16 units, AB is 8 units in length.
To find the measure of angle ABR, we need to first find the measure of angle ABQ. From the information given in the question, we know that angle Q is 38 degrees. Since angle AQB is a straight angle (180 degrees), we can calculate the measure of angle ABQ as follows:
ABQ = 180 degrees - Q
ABQ = 180 degrees - 38 degrees
ABQ = 142 degrees
Since AB is parallel to RP, and ABQ is an interior angle formed by a transversal (RQ) intersecting these parallel lines, we can conclude that angle ABR and angle ABQ are alternate interior angles. According to the Alternate Interior Angles Theorem, when two parallel lines are intersected by a transversal, alternate interior angles are congruent.
Therefore, the measure of angle ABR is equal to the measure of angle ABQ, which is 142 degrees.
So, the measure of angle ABR in triangle PQR is 142 degrees.