Chapter 2.6, Problem 1CE

a.

To determine

To find: two angles that are congruent if $\angle 6$ is complementary to $\angle 10$ and $\angle 7$ is complementary to $\angle 10$

Answer to Problem 1CE

  $\angle 6\cong \angle 7$

Explanation of Solution

Given information: $\angle 6$ is complementary to $\angle 10$ and $\angle 7$ is complementary to $\angle 10$

An angle $x$ is said to be a complement of angle $y$ if $x+y=90°$ .

That is complementary angles add up to 90 degrees.

It’s given that $\angle 6$ is complementary to $\angle 10$ and $\angle 7$ is complementary to $\angle 10$ .

As $\angle 6,\angle 7$ are complement of the same angle $\angle 10$ ,

  $\angle 6\cong \angle 7$

b.

To determine

To state: theorem, definition that justifies that $\angle 6\cong \angle 7$

Explanation of Solution

An angle $x$ is said to be a complement of angle $y$ if $x+y=90°$

If 2 angles are complements of the same angle then the 2 angles are equal or congruent.

Here,

  $\angle 6,\angle 7$ are complement of the same angle $\angle 10$

That’s why it has been said that $\angle 6\cong \angle 7$