Measuring angles in triangles worksheet with eight problems to find the missing angle 'a°' using triangle angle sum properties.

Here are the step-by-step solutions for finding the missing angles in each triangle.

Key Rule to Remember: The three angles inside any triangle always add up to 180°.
* For isosceles triangles (triangles with two equal sides marked with lines), the two angles opposite those sides are also equal.
* Angles on a straight line add up to 180°.

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Problem 1
* We have angles: $70^\circ$, $35^\circ$, and $a^\circ$.
* Add the known angles: $70 + 35 = 105$.
* Subtract from 180: $180 - 105 = 75$.
* $a = 75$

Problem 2
* We have angles: $82^\circ$, $44^\circ$, and $a^\circ$.
* Add the known angles: $82 + 44 = 126$.
* Subtract from 180: $180 - 126 = 54$.
* $a = 54$

Problem 3
* We have angles: $117^\circ$, $17^\circ$, and $a^\circ$.
* Add the known angles: $117 + 17 = 134$.
* Subtract from 180: $180 - 134 = 46$.
* $a = 46$

Problem 4
* This is an isosceles triangle (marked with tick marks on two sides). This means the two base angles are equal.
* One base angle is given as $68^\circ$, so the other base angle is also $68^\circ$.
* Add the base angles: $68 + 68 = 136$.
* Subtract from 180 to find the top angle $a$: $180 - 136 = 44$.
* $a = 44$

Problem 5
* This is an isosceles triangle. The tick marks show that the side adjacent to the $42^\circ$ angle is equal to the side adjacent to angle $a$. Wait, let's look closer at the markings.
* The tick marks are on the bottom side and the right side. This means the angles *opposite* these sides are equal.
* The angle opposite the bottom side is the top-right angle. The angle opposite the right side is the bottom-left angle ($42^\circ$).
* Therefore, the top-right angle is also $42^\circ$.
* Now we have two angles: $42^\circ$ and $42^\circ$.
* Add them: $42 + 42 = 84$.
* Subtract from 180 to find $a$: $180 - 84 = 96$.
* $a = 96$

Problem 6
* This is an equilateral triangle because all three sides have tick marks.
* In an equilateral triangle, all three angles are equal.
* Divide 180 by 3: $180 / 3 = 60$.
* $a = 60$

Problem 7
* First, find the third angle inside the triangle.
* Known internal angles: $40^\circ$ and $17^\circ$.
* Sum: $40 + 17 = 57$.
* Third internal angle: $180 - 57 = 123^\circ$.
* Angle $a$ and this $123^\circ$ angle form a straight line (linear pair).
* Straight line = $180^\circ$.
* $a = 180 - 123 = 57$.
* *(Alternative method: The exterior angle of a triangle is equal to the sum of the two opposite interior angles. So, $a = 40 + 17 = 57$)*.
* $a = 57$

Problem 8
* First, find the third angle inside the triangle.
* Known internal angles: $88^\circ$ and $39^\circ$.
* Sum: $88 + 39 = 127$.
* Third internal angle (bottom left): $180 - 127 = 53^\circ$.
* Angle $a$ and this $53^\circ$ angle form a straight line.
* $a = 180 - 53 = 127$.
* *(Alternative method: Exterior angle equals sum of opposite interior angles. $a = 88 + 39 = 127$)*.
* $a = 127$

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Final Answer:
1) 75
2) 54
3) 46
4) 44
5) 96
6) 60
7) 57
8) 127