Sum and Difference of Angles: Generate a random angle

To find the size of the missing angle, we will use the property that the sum of angles on a straight line is $180^\circ$. Given that one angle is $80^\circ$, we can calculate the missing angle using the following steps:

• Step 1: Recognize that the given angle $\alpha = 80^\circ$ and the missing angle $\beta$ form a straight line.
• Step 2: Use the angle sum property for a straight line: $\alpha + \beta = 180^\circ$
• Step 3: Substitute the known value: $80^\circ + \beta = 180^\circ$
• Step 4: Solve for the missing angle $\beta$: $\beta = 180^\circ - 80^\circ = 100^\circ$

Therefore, the size of the missing angle is $100^\circ$.

We can see from the diagram that angle DBC equals 100 degrees.

We can also see that the size of angle ABC is shown and equals 40 degrees.

Therefore, the answer is 40.

In order to calculate the value of angle ABC, we must calculate the sum of all the given angles.

That is:

$ABC=60+50$

$ABC=110$

The unmarked angle is adjacent to an angle of 160 degrees.

Remember: the sum of adjacent angles is 180 degrees.

Therefore, the size of the unknown angle is:

$180-160=20$

In order to calculate the value of angle ABC, we will begin by calculating the sum of all the given angles.

That is:

$ABC=70+20+18$

$ABC=108$

To solve this problem, we will apply the triangle sum theorem:

• Step 1: Identify the triangle formed by the known angles and the unknown angle $X$.
• Step 2: Use the triangle angle sum property which states: The sum of the angles in a triangle is $180^\circ$.
• Step 3: The known angles in the problem are $41^\circ$ and $45^\circ$.

Now, let's complete the steps:

Step 1: The angles presented form a triangle involving the angles $41^\circ$, $45^\circ$, and $X$.
Step 2: Apply the triangle angle sum theorem: $41^\circ + 45^\circ + X = 180^\circ$.
Step 3: Simplifying this we get:

$41 + 45 + X = 180$

$86 + X = 180$

Solve for $X$:

$X = 180 - 86$

$X = 94$

Therefore, the value of angle $X$ is $94^\circ$.