Question

current skill $ find the measures of the following angles in the rectangle. rectangle with diagonals intersecting, angles labeled 1, 2, 3, 4, 5 and one angle labeled 37°

Explanation:

Step1: Find angle 1

Angle 1 and 37° form a straight line: $180^\circ - 37^\circ = 143^\circ$

Step2: Find angle 2

Rectangle diagonals are equal and bisect each other, so triangle with angle 2 is isosceles. Angle adjacent to 37° in triangle: $90^\circ - 37^\circ = 53^\circ$, so angle 2 = $53^\circ$

Step3: Find angle 3

Angle 3 = angle 2 (alternate interior angles) = $53^\circ$

Step4: Find angle 4

Angle 4 = angle 3 (congruent triangles in rectangle) = $53^\circ$

Step5: Find angle 5

Triangle with angle 5 has right angle: $90^\circ - angle4 = 90^\circ -53^\circ=37^\circ$

Answer:

Angle1: $143^\circ$, Angle2: $53^\circ$, Angle3: $53^\circ$, Angle4: $53^\circ$, Angle5: $37^\circ$