Video Transcript
In the given figure, if 𝐿𝑀𝑁𝑂 is
a rectangle, 𝐴𝑁 equals 𝐵𝑀, and the measure of angle 𝑁𝑀𝐶 equals 50 degrees,
find the measure of angle 𝑀𝑁𝐶.
Since 𝐿𝑀𝑁𝑂 is a rectangle, all
of its internal angles are right angles. This means that the complementary
angles at 𝐿 and 𝑂 are also right angles. Therefore, 𝐴𝑁𝑂 and 𝐵𝐿𝑀 are a
pair of right triangles with congruent hypotenuses. Since 𝐿𝑀𝑁𝑂 is a rectangle,
segments 𝐿𝑀 and 𝑂𝑁 are also congruent. But 𝐴𝑁𝑂 and 𝐵𝐿𝑀 are right
triangles. So the Pythagorean theorem now
fixes the length of the third side in each triangle.
We can conclude that triangles
𝐴𝑁𝑂 and 𝐵𝐿𝑀 are congruent. It follows immediately that angles
𝑁𝑀𝐶 and 𝑀𝑁𝐶 are congruent. That is, angle 𝑀𝑁𝐶 has measure
50 degrees.
