Here are the step-by-step solutions for each problem on your worksheet.
1.
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Reasoning: The angle labeled $x^\circ$ is made up of two smaller angles next to each other: $35^\circ$ and $20^\circ$. To find the total size, you add them together.
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Calculation: $35 + 20 = 55$
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Answer: $x = 55$
2.
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Reasoning: Angles around a single point always add up to $360^\circ$ (a full circle). We know two of the angles ($80^\circ$ and $50^\circ$), so we subtract them from $360^\circ$ to find $a$.
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Calculation: $360 - 80 - 50 = 230$
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Answer: $a = 230$
3.
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Reasoning: Similar to question 2, these angles go all the way around a point, totaling $360^\circ$. We subtract the known angles ($150^\circ$ and $95^\circ$) from the total.
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Calculation: $360 - 150 - 95 = 115$
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Answer: $a = 115$
4.
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Reasoning: When two straight lines cross, the angles opposite each other (called vertically opposite angles) are equal. Angle $c$ is opposite the $100^\circ$ angle.
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Calculation: $c = 100$
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Answer: $c = 100$
5.
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Reasoning: Angles on a straight line add up to $180^\circ$. Angle $y$ and the $85^\circ$ angle sit on a straight line together.
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Calculation: $180 - 85 = 95$
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Answer: $y = 95$
6.
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Reasoning: The square symbol in the corner means it is a right angle, which equals $90^\circ$. The angle $x$ and the $25^\circ$ angle fit together to make that $90^\circ$ corner.
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Calculation: $90 - 25 = 65$
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Answer: $x = 65$
7.
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Reasoning: The shape is a rectangle, so every corner is $90^\circ$. In the bottom-left corner, the angle is split into $62^\circ$ and $a^\circ$. They must add up to $90^\circ$.
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Calculation: $90 - 62 = 28$
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Answer: $a = 28$
8.
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Reasoning: The arrows on the vertical lines show they are parallel. The diagonal line crossing them is a transversal. Angle $\beta$ and the $45^\circ$ angle are "alternate interior angles" (they form a Z shape), which means they are equal.
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Calculation: $\beta = 45$
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Answer: $\beta = 45$
9.
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Reasoning: The two angles are vertically opposite (opposite each other where lines cross), so they are equal. We can set up an equation: $2a = 100$. To find $a$, divide by 2.
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Calculation: $100 \div 2 = 50$
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Answer: $a = 50$
10.
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Reasoning:
* First, find $b$: Angles on a straight line add to $180^\circ$. So, $b + 155 = 180$. ($180 - 155 = 25$). So, $b = 25$.
* Next, find $a$: Angle $a$ and the $155^\circ$ angle are vertically opposite, so they are equal. So, $a = 155$.
*
Answer: $a = 155, b = 25$
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Final Answer:
1. x = 55
2. a = 230
3. a = 115
4. c = 100
5. y = 95
6. x = 65
7. a = 28
8. β = 45
9. a = 50
10. a = 155, b = 25
Parent Tip: Review the logic above to help your child master the concept of angle review worksheet.
