Imagine looking at a simple drawing with just a few lines and angles.
At first glance, it looks like a trick from a math test.
The challenge asks you to find a missing angle marked with a red question mark.
It even adds a bold rule at the top: “No pen! No paper!!”
This means you have to solve the whole puzzle using only your mind.
Let us walk through the steps together to find the correct answer easily.
First, let us look carefully at the drawing on the page.
We have a horizontal line at the bottom that forms the base.
There is a straight line going up to the left, forming an angle of 100 degrees on the outside left.
There is another line sloping down to the right, forming an angle of 160 degrees on the outside right.
These two sloping lines meet each other inside to form a triangle.
Our goal is to find the angle at the top corner inside that triangle.
To solve this, we need to remember one basic rule about straight lines.
A completely straight line always forms an angle of 180 degrees.
When a line is divided into two parts, those two parts must add up to 180 degrees.
Let us find the bottom-left inside angle of the triangle first.
The outside angle on the left is 100 degrees.
Since the total angle on that straight line is 180 degrees, we subtract 100 from 180.
180° – 100° = 80°
So, the bottom-left inside angle of the triangle is 80 degrees.
Now, let us find the bottom-right inside angle of the triangle.
The outside angle on the right side is 160 degrees.
Using the same straight line rule, we subtract 160 from 180.
180° – 160° = 20°
So, the bottom-right inside angle of the triangle is 20 degrees.
Next, we look at the shape formed inside by the three lines.
It is a simple triangle with three corners.
Another key rule in geometry is that all three inside angles of any triangle always add up to 180 degrees.
We already know two of these inside angles: 80 degrees and 20 degrees.
Let us add these two angles together.
80° + 20° = 100°
Now, to find the third inside angle at the top, we subtract 100 from 180.
180° – 100° = 80°
This means the top inside angle of the triangle is 80 degrees.
Finally, we are ready to find the missing angle with the red question mark.
Look closely at the top corner where the red arc is drawn.
The line passing through that corner is a single straight line.
The top inside angle of the triangle and the missing angle sit right next to each other on this straight line.
Together, they must add up to 180 degrees.
Since the top inside angle is 80 degrees, we subtract 80 from 180 to get the missing angle.
180° – 80° = 100°
The missing angle marked with the red question mark is exactly 100 degrees!