# Grade 10: A triangle has 90° and 48° angles — how big is the third angle?

## Question

Here is the question : GRADE 10: A TRIANGLE HAS 90° AND 48° ANGLES — HOW BIG IS THE THIRD ANGLE?

## Option

Here is the option for the question :

• 48°
• 42°
• 36°
• 24°

And, the answer for the the question is :

42°

## Explanation:

In geometry class in the tenth grade, students learn about trigonometry, or the study of angles.

In Grade 10 geometry, understanding the properties and relationships of angles is crucial when analyzing and solving problems related to triangles. One common problem involves determining the measure of an unknown angle in a triangle when the measures of other angles are given. Let’s explore a scenario where a triangle has angles measuring 90° and 48°, and we need to find the measure of the third angle. By applying the principles of triangle geometry and angle relationships, we can deduce that the third angle measures 42°.

To understand the process of finding the measure of the third angle in a triangle, we must first grasp a fundamental concept: the sum of the interior angles of any triangle is always 180°. This property allows us to establish a relationship among the angles within a triangle.

In the given scenario, we are provided with two angles: a 90° angle and a 48° angle. To find the measure of the third angle, we can subtract the sum of these two known angles from 180°. Let’s calculate it step by step:

180° – (90° + 48°) = 180° – 138° = 42°

Hence, the measure of the third angle in the given triangle is 42°. This means that when the 90° and 48° angles are combined with the 42° angle, the sum of the interior angles of the triangle will be 180°, as expected.

Understanding angle relationships within triangles is fundamental in geometry. The concept of the sum of interior angles applies to all triangles, regardless of their size, shape, or orientation. By recognizing and utilizing this relationship, Grade 10 geometry students can solve various problems involving triangles and their angles.

The measure of the third angle in a triangle is not only a mathematical curiosity but also an important concept with practical applications. Triangle geometry finds its application in fields such as architecture, engineering, and design. Understanding the measures and relationships of angles helps professionals in these fields create structures that are both aesthetically pleasing and structurally sound.

Moreover, comprehending the properties of triangles and their angles lays the foundation for advanced geometric concepts. Students who master the principles of triangle geometry in Grade 10 will build a strong mathematical base that will benefit them in higher-level mathematics courses, such as trigonometry and calculus.

in a triangle with angles measuring 90° and 48°, the measure of the third angle is determined to be 42°. This determination is made by applying the fundamental concept that the sum of the interior angles of any triangle is always 180°. By subtracting the sum of the known angles from 180°, we can find the measure of the unknown angle. Understanding angle relationships within triangles is essential in geometry and has practical applications in various fields. By mastering these concepts, Grade 10 students can develop their problem-solving skills and lay a solid foundation for future mathematical pursuits.

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