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!
