To find the unknown angles, we use the rule that the sum of all angles inside a triangle is always
180°.
Here is the step-by-step solution for each problem:
1.
* Given angles: $18^\circ$ and $145^\circ$.
* Add them together: $18 + 145 = 163$.
* Subtract from 180: $180 - 163 = 17$.
*
$x = 17$
2.
* Given angles: $85^\circ$ and $55^\circ$.
* Add them together: $85 + 55 = 140$.
* Subtract from 180: $180 - 140 = 40$.
*
$x = 40$
3.
* Given angles: $70^\circ$ and $70^\circ$.
* Add them together: $70 + 70 = 140$.
* Subtract from 180: $180 - 140 = 40$.
*
$x = 40$
4.
* Given angles: $55^\circ$ and $75^\circ$.
* Add them together: $55 + 75 = 130$.
* Subtract from 180: $180 - 130 = 50$.
*
$x = 50$
5.
* The diagonal line splits the square into two triangles. We can look at either the top-left triangle or the bottom-right triangle. Let's look at the bottom-right one.
* It has a right angle ($90^\circ$), an angle of $45^\circ$, and the unknown angle $x^\circ$.
* Add the known angles: $90 + 45 = 135$.
* Subtract from 180: $180 - 135 = 45$.
*
$x = 45$
Final Answer:
1. x = 17
2. x = 40
3. x = 40
4. x = 50
5. x = 45
Parent Tip: Review the logic above to help your child master the concept of triangle angles worksheet.
