Let's solve each of the three angle problems step by step, based on the relationships described in the image.
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Problem 1: Supplementary Angles
Given:
- Two angles form a straight line.
- One angle is $42^\circ$, and the other is $x^\circ$.
- The two angles are
supplementary, meaning they add up to $180^\circ$.
Equation:
$$
x + 42 = 180
$$
Solve for $x$:
$$
x = 180 - 42 = 138
$$
✔ So, $x = 138^\circ$
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Problem 2: Vertical Angles
Given:
- Two intersecting lines form four angles.
- One angle is $28^\circ$, and the opposite angle is $y^\circ$.
- These are
vertical angles, which are always equal.
Conclusion:
$$
y = 28^\circ
$$
✔ So, $y = 28^\circ$
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Problem 3: Complementary Angles
Given:
- A right triangle (implied by the context of complementary angles).
- One angle is $64^\circ$, and the other is $z^\circ$.
- The two angles are
complementary, meaning they add up to $90^\circ$.
Equation:
$$
z + 64 = 90
$$
Solve for $z$:
$$
z = 90 - 64 = 26
$$
✔ So, $z = 26^\circ$
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✔ Final Answers:
- $x = 138^\circ$
- $y = 28^\circ$
- $z = 26^\circ$
These solutions use basic angle relationships:
-
Supplementary angles: sum to $180^\circ$
-
Vertical angles: are equal
-
Complementary angles: sum to $90^\circ$
Parent Tip: Review the logic above to help your child master the concept of finding missing angles worksheet 7th grade.
