Question

find the measures of the following angles in the rectangle.

m∠1=

m∠2=

m∠3=

m∠4=

m∠5=

Explanation:

Step1: Use properties of rectangle

In a rectangle, opposite sides are parallel and diagonals are equal and bisect each other. Also, each angle in a rectangle is \(90^{\circ}\).

Step2: Find \(m\angle1\)

Since the diagonals of a rectangle bisect each other, \(\angle1\) and the \(21^{\circ}\) angle are alternate - interior angles (because of parallel sides of the rectangle). So \(m\angle1 = 21^{\circ}\).

Step3: Find \(m\angle2\)

In a right - triangle formed in the rectangle (right - angled at the corner of the rectangle), if one angle is \(21^{\circ}\), then \(m\angle2=90^{\circ}-21^{\circ}=69^{\circ}\).

Step4: Find \(m\angle3\)

\(\angle3\) and \(\angle1\) are alternate - interior angles (because of parallel sides of the rectangle). So \(m\angle3 = 21^{\circ}\).

Step5: Find \(m\angle4\)

\(\angle4\) and \(\angle2\) are alternate - interior angles (because of parallel sides of the rectangle). So \(m\angle4 = 69^{\circ}\).

Step6: Find \(m\angle5\)

\(\angle5\) is the sum of \(\angle1\) and \(\angle3\) (exterior angle property of a triangle). So \(m\angle5=21^{\circ}+21^{\circ}=42^{\circ}\).

Answer:

\(m\angle1 = 21^{\circ}\), \(m\angle2 = 69^{\circ}\), \(m\angle3 = 21^{\circ}\), \(m\angle4 = 69^{\circ}\), \(m\angle5 = 42^{\circ}\)