A trapezoid with congruent base angles must be
square
parallelogram
rectangle
isosceles trapezoid
No classification is guaranteed
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isosceles trapezoid
Find m∠BAC in the figure shown below.
Line upper D upper C is shown intersecting with line upper E upper B at point upper A. The angle upper E upper A upper D is labeled 80 degrees.
A. m∠BAC=80°
B. m∠BAC=100°
C. m∠BAC=10°
D. m∠BAC=50°
Since angle ABC and angle ABD are supplementary (they form a straight line), we can find m∠ABC by subtracting 80° (given angle) from 180° (sum of angles in triangle ABD).
m∠ABC = 180° - 80° = 100°
Similarly, angles ABC and BAC are supplementary, so:
m∠BAC = 180° - m∠ABC = 180° - 100° = 80°
Therefore, the answer is A. m∠BAC=80°.
An angle measures 47°. What are the measures of the angle’s complement?
A. 43°
B. 133°
C. 53°
D. 143°
Since the complement of an angle is the angle that when added to it results in a sum of 90°, we can find the measure of the complement of 47° by subtracting 47 from 90:
90° - 47° = 43°
Therefore, the answer is A. 43°.
Which of the following correctly identifies angles that add up to 90° and 180°?
A. adjacent angles, congruent angles
B. complementary angles, vertical angles
C. supplementary angles, complementary angles
D. vertical angles, adjacent angles
B. complementary angles, vertical angles.
Complementary angles add up to 90° and are angles that complement each other, while vertical angles are opposite to each other and have the same measure.
Identify the correct ways to classify ∠1 and ∠4 in the figure shown below.
A horizontal line is intersected at a right angle at the endpoint of a ray pointing up. Another line goes through the intersection point from upper left to lower right. Angle 1 is left of this line and right of the ray. Angle 2 is left or ray and above horizontal line. Angle 5 is below horizontal line and right of slanted line. Angle 3 is right of slanted line and below horizontal line. Angle 4 is above horizontal line and left of slanted line.
A. adjacent, supplementary
B. adjacent, complementary
C. adjacent, congruent
D. vertical, complementary
A. adjacent, supplementary.
Angles 1 and 2 are adjacent because they share a common vertex and a common side, and angles 3 and 4 are adjacent for the same reasons.
Angles 1 and 2 form a straight line, so they are supplementary (add up to 180°), and angles 3 and 4 also form a straight line and are therefore supplementary.
Therefore, the correct classification is adjacent, supplementary for both angles 1 and 4.