8th Grade Math Worksheets - Free Printable

$8th Grade Math Worksheets$

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To solve the problem of finding the measure of the indicated angles in each triangle, we need to use the properties of triangles, specifically the fact that the sum of the interior angles of a triangle is always 180°. Let's go through each problem step by step.

---

Problem 1:

#### Triangle with angles $ m\angle C $, $ 60^\circ $, and $ 70^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 60^\circ $ and $ 70^\circ $.
- Let $ m\angle C = x $.

Using the angle sum property:
\[
x + 60^\circ + 70^\circ = 180^\circ
\]
\[
x + 130^\circ = 180^\circ
\]
\[
x = 180^\circ - 130^\circ
\]
\[
x = 50^\circ
\]

Thus, $ m\angle C = 50^\circ $.

---

Problem 2:

#### Right triangle with one angle $ 90^\circ $ and another angle $ 45^\circ $

- In a right triangle, one angle is always $ 90^\circ $.
- Given angles: $ 90^\circ $ and $ 45^\circ $.
- Let $ m\angle B = x $.

Using the angle sum property:
\[
x + 90^\circ + 45^\circ = 180^\circ
\]
\[
x + 135^\circ = 180^\circ
\]
\[
x = 180^\circ - 135^\circ
\]
\[
x = 45^\circ
\]

Thus, $ m\angle B = 45^\circ $.

---

Problem 3:

#### Triangle with angles $ m\angle D $, $ 50^\circ $, and $ 60^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 50^\circ $ and $ 60^\circ $.
- Let $ m\angle D = x $.

Using the angle sum property:
\[
x + 50^\circ + 60^\circ = 180^\circ
\]
\[
x + 110^\circ = 180^\circ
\]
\[
x = 180^\circ - 110^\circ
\]
\[
x = 70^\circ
\]

Thus, $ m\angle D = 70^\circ $.

---

Problem 4:

#### Triangle with angles $ m\angle F $, $ 75^\circ $, and $ 30^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 75^\circ $ and $ 30^\circ $.
- Let $ m\angle F = x $.

Using the angle sum property:
\[
x + 75^\circ + 30^\circ = 180^\circ
\]
\[
x + 105^\circ = 180^\circ
\]
\[
x = 180^\circ - 105^\circ
\]
\[
x = 75^\circ
\]

Thus, $ m\angle F = 75^\circ $.

---

Problem 5:

#### Triangle with angles $ m\angle V $, $ 110^\circ $, and $ 30^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 110^\circ $ and $ 30^\circ $.
- Let $ m\angle V = x $.

Using the angle sum property:
\[
x + 110^\circ + 30^\circ = 180^\circ
\]
\[
x + 140^\circ = 180^\circ
\]
\[
x = 180^\circ - 140^\circ
\]
\[
x = 40^\circ
\]

Thus, $ m\angle V = 40^\circ $.

---

Problem 6:

#### Triangle with angles $ m\angle N $, $ 80^\circ $, and $ 50^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 80^\circ $ and $ 50^\circ $.
- Let $ m\angle N = x $.

Using the angle sum property:
\[
x + 80^\circ + 50^\circ = 180^\circ
\]
\[
x + 130^\circ = 180^\circ
\]
\[
x = 180^\circ - 130^\circ
\]
\[
x = 50^\circ
\]

Thus, $ m\angle N = 50^\circ $.

---

Problem 7:

#### Triangle with angles $ m\angle T $, $ 40^\circ $, and $ 70^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 40^\circ $ and $ 70^\circ $.
- Let $ m\angle T = x $.

Using the angle sum property:
\[
x + 40^\circ + 70^\circ = 180^\circ
\]
\[
x + 110^\circ = 180^\circ
\]
\[
x = 180^\circ - 110^\circ
\]
\[
x = 70^\circ
\]

Thus, $ m\angle T = 70^\circ $.

---

Problem 8:

#### Triangle with angles $ m\angle E $, $ 65^\circ $, and $ 55^\circ $

- The sum of the interior angles of a triangle is $ 180^\circ $.
- Given angles: $ 65^\circ $ and $ 55^\circ $.
- Let $ m\angle E = x $.

Using the angle sum property:
\[
x + 65^\circ + 55^\circ = 180^\circ
\]
\[
x + 120^\circ = 180^\circ
\]
\[
x = 180^\circ - 120^\circ
\]
\[
x = 60^\circ
\]

Thus, $ m\angle E = 60^\circ $.

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{1. } m\angle C = 50^\circ \\
&\text{2. } m\angle B = 45^\circ \\
&\text{3. } m\angle D = 70^\circ \\
&\text{4. } m\angle F = 75^\circ \\
&\text{5. } m\angle V = 40^\circ \\
&\text{6. } m\angle N = 50^\circ \\
&\text{7. } m\angle T = 70^\circ \\
&\text{8. } m\angle E = 60^\circ
\end{aligned}
}
\]

Parent Tip: Review the logic above to help your child master the concept of 8th grade math worksheet printable.

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