This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the answers based on the provided image: Step 1: Classify the angle for question 14. The angle shown next to "14." is visually larger than 90^ but less than 180^. 14. The angle shown is an obtuse angle. Step 2: Calculate and classify H M J. From the diagram, the measure of H M J is given as 60^. Since 60^ < 90^, it is an acute angle. H M J = 60^ (Acute angle) Step 3: Calculate and classify J M K. From the diagram, the measure of J M K is given as 30^. Since 30^ < 90^, it is an acute angle. J M K = 30^ (Acute angle) Step 4: Calculate and classify H M K. H M K is the sum of H M J and J M K. H M K = H M J + J M K H M K = 60^ + 30^ H M K = 90^ Since H M K = 90^, it is a right angle. H M K = 90^ (Right angle) Step 5: Calculate and classify L M J. Let L be the point on the leftmost ray. L M J is the sum of L M H and H M J. L M J = L M H + H M J L M J = 50^ + 60^ L M J = 110^ Since 90^ < 110^ < 180^, it is an obtuse angle. L M J = 110^ (Obtuse angle) Step 6: Calculate and classify L M N. Let L be the point on the leftmost ray and N be the point on the rightmost ray. L M N is the sum of all angles along the straight line. L M N = L M H + H M J + J M K + K M N L M N = 50^ + 60^ + 30^ + 40^ L M N = 180^ Since L M N = 180^, it is a straight angle. L M N = 180^ (Straight angle) Last free one today — make it count tomorrow, or type /upgrade for unlimited.