Fill in the blank to make each of the statements true. Write your answers in your notebook.

1. If [tex]\( \angle Z \)[/tex] and [tex]\( \angle L \)[/tex] are complementary angles and [tex]\( m\angle Z = 35^\circ \)[/tex], then [tex]\( m\angle L = \)[/tex] _____.

2. If [tex]\( \angle A \)[/tex] and [tex]\( \angle M \)[/tex] are supplementary angles and [tex]\( m\angle M = 35^\circ \)[/tex], then [tex]\( m\angle A = \)[/tex] _____.

3. If two angles are congruent and complementary, then the measure of each angle is _____.

Remember: Vertical angles are congruent, and angles forming a linear pair are always supplementary.



Answer :

Certainly! Let’s go through each statement step-by-step to fill in the blanks.

1. If ZZ and ZL are complementary angles and mZZ = 35°, then mZL =

Complementary angles are two angles whose measures add up to 90°. Given that the measure of ZZ (mZZ) is 35°, we need to find the measure of ZL (mZL).

To find mZL, subtract mZZ from 90°:

[tex]\[ mZL = 90° - 35° = 55° \][/tex]

Therefore, the answer to the first statement is:

[tex]\[ mZL = 55° \][/tex]


2. If ZA and M are supplementary angles and mZzM= 35°, then mZA =

Supplementary angles are two angles whose measures add up to 180°. Given that the measure of ZM (mZzM) is 35°, we need to find the measure of ZA (mZA).

To find mZA, subtract mZzM from 180°:

[tex]\[ mZA = 180° - 35° = 145° \][/tex]

Therefore, the answer to the second statement is:

[tex]\[ mZA = 145° \][/tex]


3. If two angles are congruent and complementary, then the measure of each angle is

Congruent angles are angles that have the same measure. Complementary angles add up to 90°. If two angles are both congruent and complementary, it means they must each measure half of 90°:

[tex]\[ \text{Measure of each angle} = \frac{90°}{2} = 45° \][/tex]

Therefore, the answer to the third statement is:

[tex]\[ \text{Measure of each angle} = 45° \][/tex]


So, here are the filled-in statements:

1. If ZZ and ZL are complementary angles and mZZ = 35°, then mZL = 55°
2. If ZA and M are supplementary angles and mZzM= 35°, then mZA = 145°
3. If two angles are congruent and complementary, then the measure of each angle is 45°

Write down these answers in your notebook!