Question

In the graphs below, triangle ABC has been rotated to create triangle DEF.Triangle ABC is right angle, with a measure of 23° for acute angle B.What are the measures of each right angle in triangle DEF?m

Answer 1

Given data:

The given figure of the triangles in which the ∠B=23 degrees.

The measure of the ∠C=90 degrees,

The expression for the sum of angles of triangle is,

∠A+∠B+∠C=180 degrees

∠A+23+90=180

∠A=67 degrees

When the given figure is rotated the side,

AC=DF

AB=DE

CB=FE

The expression for the angles is,

m∠D=m∠A

=67 degree

m∠E=m∠B

=23 degree

m∠F=m∠C

=90 degree

Thus, the mmeasure of the angle D is 67 degrees, the mmeasure of the angle E is 23 degrees, and the measure of the angle CF is 90 degrees.