Measures Of Two Angles P And Q Of A Angle PQR Are 43° And 48°. Find The Measure Of The Third Angle

Mar 9, 2025 by ADMIN 101 views

**Measures of Two Angles P and Q of a Triangle PQR**

Introduction

In geometry, a triangle is a polygon with three sides and three angles. The sum of the measures of the interior angles of a triangle is always 180°. In this article, we will discuss how to find the measure of the third angle of a triangle when the measures of two angles are given.

The Sum of the Measures of the Interior Angles of a Triangle

The sum of the measures of the interior angles of a triangle is a fundamental concept in geometry. It states that the sum of the measures of the interior angles of a triangle is always 180°. This can be expressed mathematically as:

∠P + ∠Q + ∠R = 180°

where ∠P, ∠Q, and ∠R are the measures of the interior angles of the triangle.

Finding the Measure of the Third Angle

Now, let's consider a triangle PQR with measures of two angles P and Q as 43° and 48°, respectively. We need to find the measure of the third angle R.

Step 1: Write the Equation

Using the formula ∠P + ∠Q + ∠R = 180°, we can write the equation as:

43° + 48° + ∠R = 180°

Step 2: Simplify the Equation

Now, let's simplify the equation by adding the measures of angles P and Q:

91° + ∠R = 180°

Step 3: Solve for ∠R

To solve for ∠R, we need to isolate the variable ∠R on one side of the equation. We can do this by subtracting 91° from both sides of the equation:

∠R = 180° - 91°

∠R = 89°

Therefore, the measure of the third angle R is 89°.

Conclusion

In this article, we discussed how to find the measure of the third angle of a triangle when the measures of two angles are given. We used the formula ∠P + ∠Q + ∠R = 180° and simplified the equation to find the measure of the third angle R. The measure of the third angle R is 89°.

Example Problems

Find the measure of the third angle of a triangle with measures of two angles as 25° and 35°.
Find the measure of the third angle of a triangle with measures of two angles as 40° and 50°.

Answer Key

The measure of the third angle is 110°.
The measure of the third angle is 90°.

Tips and Tricks

Always use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle.
Simplify the equation by adding or subtracting the measures of angles P and Q.
Isolate the variable ∠R on one side of the equation to solve for ∠R.

Frequently Asked Questions

What is the sum of the measures of the interior angles of a triangle?
How do I find the measure of the third angle of a triangle when the measures of two angles are given?

Answer

The sum of the measures of the interior angles of a triangle is always 180°.
Use the formula ∠P + ∠Q + ∠R = 180° and simplify the equation to find the measure of the third angle.
Measures of Two Angles P and Q of a Triangle PQR =====================================================

Q&A: Measures of Two Angles P and Q of a Triangle PQR

Introduction

In our previous article, we discussed how to find the measure of the third angle of a triangle when the measures of two angles are given. In this article, we will answer some frequently asked questions related to the measures of two angles P and Q of a triangle PQR.

Q1: What is the sum of the measures of the interior angles of a triangle?

A1: The sum of the measures of the interior angles of a triangle is always 180°.

Q2: How do I find the measure of the third angle of a triangle when the measures of two angles are given?

A2: To find the measure of the third angle of a triangle when the measures of two angles are given, use the formula ∠P + ∠Q + ∠R = 180° and simplify the equation to find the measure of the third angle.

Q3: What if the measures of two angles are not given? How do I find the measure of the third angle?

A3: If the measures of two angles are not given, you cannot find the measure of the third angle using the formula ∠P + ∠Q + ∠R = 180°. However, you can use other methods such as the Law of Sines or the Law of Cosines to find the measure of the third angle.

Q4: Can I use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle if the triangle is not a right triangle?

A4: Yes, you can use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle even if the triangle is not a right triangle.

Q5: What if the measures of two angles are not integers? How do I find the measure of the third angle?

A5: If the measures of two angles are not integers, you can still use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle. However, you may need to use a calculator to simplify the equation.

Q6: Can I use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle if the triangle is an obtuse triangle?

A6: Yes, you can use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle even if the triangle is an obtuse triangle.

Q7: What if the measures of two angles are equal? How do I find the measure of the third angle?

A7: If the measures of two angles are equal, you can use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle. Since the measures of two angles are equal, you can substitute the measures of two angles with the same value.

Q8: Can I use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle if the triangle is an equilateral triangle?

A8: Yes, you can use the formula ∠P + ∠Q + ∠R = 180° to find the measure of the third angle even if the triangle is an equilateral triangle.