Find the missing angle in a triangle (examples, solutions, videos ... - Free Printable

To solve the problem of finding the missing angles in the given triangles, we will use the properties of triangles and supplementary angles. Let's go through each triangle step by step.

---

Triangle 1:

The triangle has angles of \(45^\circ\) and \(70^\circ\), and we need to find the missing angle \(x\).

#### Step 1: Use the Triangle Angle Sum Property
The sum of the interior angles of a triangle is always \(180^\circ\).

\[
45^\circ + 70^\circ + x = 180^\circ
\]

#### Step 2: Solve for \(x\)
\[
115^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 115^\circ
\]
\[
x = 65^\circ
\]

So, the missing angle \(x\) is:
\[
\boxed{65^\circ}
\]

---

Triangle 2:

The triangle has one angle of \(110^\circ\) and two equal angles \(x\). We need to find the value of \(x\).

#### Step 1: Use the Triangle Angle Sum Property
The sum of the interior angles of a triangle is \(180^\circ\).

\[
110^\circ + x + x = 180^\circ
\]

#### Step 2: Simplify and Solve for \(x\)
\[
110^\circ + 2x = 180^\circ
\]
\[
2x = 180^\circ - 110^\circ
\]
\[
2x = 70^\circ
\]
\[
x = \frac{70^\circ}{2}
\]
\[
x = 35^\circ
\]

So, the missing angle \(x\) is:
\[
\boxed{35^\circ}
\]

---

Triangle 3:

The triangle has angles of \(62^\circ\) and \(51^\circ\), and we need to find the missing angles \(x\) and \(y\).

#### Step 1: Find the Third Interior Angle of the Triangle
Using the Triangle Angle Sum Property:

\[
62^\circ + 51^\circ + x = 180^\circ
\]

#### Step 2: Solve for \(x\)
\[
113^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 113^\circ
\]
\[
x = 67^\circ
\]

#### Step 3: Find the Exterior Angle \(y\)
The exterior angle \(y\) is supplementary to the interior angle \(x\):

\[
y = 180^\circ - x
\]
\[
y = 180^\circ - 67^\circ
\]
\[
y = 113^\circ
\]

So, the missing angles are:
\[
x = 67^\circ, \quad y = 113^\circ
\]

---

Triangle 4:

The triangle has an exterior angle of \(120^\circ\) and an interior angle of \(70^\circ\). We need to find the missing angles \(x\) and \(y\).

#### Step 1: Find the Interior Angle Opposite the Exterior Angle
The exterior angle is supplementary to its adjacent interior angle:

\[
x = 180^\circ - 120^\circ
\]
\[
x = 60^\circ
\]

#### Step 2: Use the Triangle Angle Sum Property
The sum of the interior angles of the triangle is \(180^\circ\):

\[
70^\circ + 60^\circ + y = 180^\circ
\]

#### Step 3: Solve for \(y\)
\[
130^\circ + y = 180^\circ
\]
\[
y = 180^\circ - 130^\circ
\]
\[
y = 50^\circ
\]

So, the missing angles are:
\[
x = 60^\circ, \quad y = 50^\circ
\]

---

Final Answers:

1. For the first triangle: \(x = \boxed{65^\circ}\)
2. For the second triangle: \(x = \boxed{35^\circ}\)
3. For the third triangle: \(x = 67^\circ, y = 113^\circ\)
4. For the fourth triangle: \(x = 60^\circ, y = 50^\circ\)