Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
in the graphs below, triangle abc has been rotated to create triangle def.

triangle abc is a right triangle, with a measure of 23° for acute angle b.
what are the measures of each angle in triangle def?
m∠d =
°
m∠e =
°
m∠f =
°

Explanation:

Step1: Use the property of rotation

Rotation preserves the shape and size of the figure. So, \(\triangle ABC\cong\triangle DEF\).

Step2: Find angles in \(\triangle ABC\)

In right - triangle \(ABC\), \(\angle C = 90^{\circ}\), \(\angle B=23^{\circ}\). Using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)), we get \(\angle A=180^{\circ}-\angle B - \angle C\). Substitute \(\angle B = 23^{\circ}\) and \(\angle C=90^{\circ}\), then \(\angle A=180^{\circ}-23^{\circ}-90^{\circ}=67^{\circ}\).

Step3: Match angles in \(\triangle DEF\)

Since \(\triangle ABC\cong\triangle DEF\), \(\angle D=\angle A\), \(\angle E=\angle B\), \(\angle F=\angle C\).

Answer:

\(m\angle D = 67\), \(m\angle E=23\), \(m\angle F = 90\)