In this page, we practice finding missing angles using the rule:
$$\text{Sum of interior angles}=180^\circ$$
Example 1 – Find One Missing Angle
Find the missing angle \(x\).
The angles of triangle \(ABC\) are:
\(A=60^\circ\)
\(B=x\)
\(C=30^\circ\)
Using the sum of the interior angles:
$$60^\circ+x+30^\circ=180^\circ$$
$$90^\circ+x=180^\circ$$
$$x=90^\circ$$
So, the missing angle is:
$$x=90^\circ$$
Example 2 – Find an Angle in a Right Triangle
Find the missing angle \(x\).
The angles of triangle \(ABC\) are:
\(A=x\)
\(B=90^\circ\)
\(C=40^\circ\)
Using the sum of the interior angles:
$$x+90^\circ+40^\circ=180^\circ$$
$$x+130^\circ=180^\circ$$
$$x=50^\circ$$
So, the missing angle is:
$$x=50^\circ$$
Example 3 – Find the Third Angle
Find the missing angle \(x\).
The angles of triangle \(ABC\) are:
\(A=50^\circ\)
\(B=100^\circ\)
\(C=x\)
Using the sum of the interior angles:
$$50^\circ+100^\circ+x=180^\circ$$
$$150^\circ+x=180^\circ$$
$$x=30^\circ$$
So, the missing angle is:
$$x=30^\circ$$
Example 4 – Find Two Equal Angles
Find \(x\), the measure of each equal angle.
The angles of triangle \(ABC\) are:
\(A=x\)
\(B=60^\circ\)
\(C=x\)
Using the sum of the interior angles:
$$x+60^\circ+x=180^\circ$$
$$2x+60^\circ=180^\circ$$
$$2x=120^\circ$$
$$x=60^\circ$$
So, each equal angle is:
$$60^\circ$$
The three angles are:
$$60^\circ,\ 60^\circ,\ 60^\circ$$
Example 5 – Find Angles Written in Terms of (x)
Find \(x\), then find the measures of angles \(D\) and \(F\).
The angles of triangle \(DEF\) are:
\(D=x\)
\(E=90^\circ\)
\(F=x-20^\circ\)
Using the sum of the interior angles:
$$x+90^\circ+(x-20^\circ)=180^\circ$$
$$2x+70^\circ=180^\circ$$
$$2x=110^\circ$$
$$x=55^\circ$$
Therefore:
$$D=x=55^\circ$$
$$F=x-20^\circ=55^\circ-20^\circ=35^\circ$$
So, the three angles are:
$$55^\circ,\ 90^\circ,\ 35^\circ$$
Example 6 – Find All Three Angles
Find \(x\), then find all three angles.
The angles of triangle \(GHI\) are:
$$G=x$$
$$H=3x$$
$$I=2x$$
Using the sum of the interior angles:
$$x+3x+2x=180^\circ$$
$$6x=180^\circ$$
$$x=30^\circ$$
Therefore:
$$G=x=30^\circ$$
$$H=3x=3(30^\circ)=90^\circ$$
$$I=2x=2(30^\circ)=60^\circ$$
So, the three angles are:
$$30^\circ,\ 90^\circ,\ 60^\circ$$
Practice
- More Examples (Current page)