Here are the step-by-step solutions for each triangle problem. Remember that the angles inside any triangle always add up to
180°. Also, angles on a straight line add up to
180°.
Problem 1
* Given angles: $70^\circ$ and $45^\circ$.
* Calculation: $180 - 70 - 45 = 65$.
*
$x = 65^\circ$
Problem 2
* Given angles: $82^\circ$ and $35^\circ$.
* Calculation: $180 - 82 - 35 = 63$.
*
$x = 63^\circ$
Problem 3
* Given angles: $58^\circ$ and $86^\circ$.
* Calculation: $180 - 58 - 86 = 36$.
*
$x = 36^\circ$
Problem 4
* First, find the third angle inside the triangle: $180 - 61 - 52 = 67^\circ$.
* Angle $x$ is on a straight line with this $67^\circ$ angle. Straight lines equal $180^\circ$.
* Calculation: $180 - 67 = 113$.
*
$x = 113^\circ$
Problem 5
* First, find angle $y$. It is on a straight line with $120^\circ$.
* $y = 180 - 120 = 60^\circ$.
* Now find $x$ using the triangle sum ($180^\circ$). The angles are $50^\circ$, $60^\circ$ ($y$), and $x$.
* $x = 180 - 50 - 60 = 70$.
*
$x = 70^\circ$ (and $y = 60^\circ$)
Problem 6
* Given angles: $77^\circ$ and $64^\circ$.
* Calculation: $180 - 77 - 64 = 39$.
*
$x = 39^\circ$
Problem 7
* Given angles: $13^\circ$ and $29^\circ$.
* Calculation: $180 - 13 - 29 = 138$.
*
$x = 138^\circ$
Problem 8
* First, find angle $q$ inside the triangle.
* $q = 180 - 64 - 38 = 78^\circ$.
* Angle $x$ and angle $q$ are on a straight line.
* $x = 180 - 78 = 102$.
*
$x = 102^\circ$ (and $q = 78^\circ$)
Problem 9
* First, find angle $x$. It is on a straight line with $69^\circ$.
* $x = 180 - 69 = 111^\circ$.
* Now find angle $y$ inside the triangle. The angles are $81^\circ$, $69^\circ$, and $y$.
* $y = 180 - 81 - 69 = 30$.
*
$x = 111^\circ$,
$y = 30^\circ$
Problem 10
* This is a right-angled triangle (the square symbol means $90^\circ$).
* Given angles: $90^\circ$ and $45^\circ$.
* Calculation: $180 - 90 - 45 = 45$.
*
$x = 45^\circ$
Problem 11
* Given angles: $35^\circ$ and $15^\circ$.
* Calculation: $180 - 35 - 15 = 130$.
*
$x = 130^\circ$
Problem 12
* This is a right-angled triangle ($90^\circ$).
* Given angles: $90^\circ$ and $45^\circ$.
* Calculation: $180 - 90 - 45 = 45$.
*
$x = 45^\circ$
Final Answer:
1. x = 65°
2. x = 63°
3. x = 36°
4. x = 113°
5. x = 70°, y = 60°
6. x = 39°
7. x = 138°
8. x = 102°, q = 78°
9. x = 111°, y = 30°
10. x = 45°
11. x = 130°
12. x = 45°
Parent Tip: Review the logic above to help your child master the concept of triangle angle sum worksheet.
