Here are the step-by-step solutions to find the missing angles.
1) Right Angle Split
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Concept: The square symbol in the corner means the total angle is $90^\circ$ (a right angle).
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Calculation: We know two parts of the angle: $35^\circ$ and $25^\circ$.
* First, add the known angles together: $35 + 25 = 60$.
* Subtract that sum from the total $90^\circ$: $90 - 60 = 30$.
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Missing Angle: $30^\circ$
2) Angles on a Straight Line
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Concept: Angles on a straight line always add up to $180^\circ$.
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Calculation: We have two known angles: $40^\circ$ and $65^\circ$.
* Add them together: $40 + 65 = 105$.
* Subtract from $180^\circ$: $180 - 105 = 75$.
*
Missing Angle: $75^\circ$
3) Angles in a Triangle
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Concept: The three angles inside any triangle always add up to $180^\circ$.
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Calculation: We have angles of $99^\circ$ and $44^\circ$.
* Add them together: $99 + 44 = 143$.
* Subtract from $180^\circ$: $180 - 143 = 37$.
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Missing Angle: $37^\circ$
4) Isosceles Triangle
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Concept: In an isosceles triangle, two of the angles are equal. Also, all three angles add up to $180^\circ$.
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Calculation: The single unique angle is $36^\circ$. This means the other two equal angles must share the remaining amount.
* Subtract the known angle from the total: $180 - 36 = 144$.
* Divide the remainder by 2 to find the size of the equal angles: $144 \div 2 = 72$.
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Missing Angles: Both missing angles are $72^\circ$.
5) Angles around a Point
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Concept: Angles that meet at a central point (like a full circle) add up to $360^\circ$.
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Calculation: We have angles of $125^\circ$ and $45^\circ$.
* Add them together: $125 + 45 = 170$.
* Subtract from $360^\circ$: $360 - 170 = 190$.
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Missing Angle: $190^\circ$
6) Angles around a Point
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Concept: Again, angles around a point add up to $360^\circ$.
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Calculation: We have three known angles: $162^\circ$, $34^\circ$, and $104^\circ$.
* Add them all together: $162 + 34 + 104 = 300$.
* Subtract from $360^\circ$: $360 - 300 = 60$.
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Missing Angle: $60^\circ$
Final Answer:
1) 30°
2) 75°
3) 37°
4) 72° (both missing angles)
5) 190°
6) 60°
Parent Tip: Review the logic above to help your child master the concept of measuring angles in triangles worksheet.
