the second angle in a triangle is five times as large as the first .the third angle is two-thirds as large as the first. find the angle measures
Answers
A square is basically four lines joined so that each line makes a 90-degree angle with the other line. In this way, a court has four 90 degree angles on its four sides.
Similarly, a straight line stretched to both sides by 180 degrees. If rotated at any point, it becomes two lines separated by a certain angle. In the same way, triangles are essentially three line segments joined at certain angle values.
These angle measures define the type of triangle. Therefore, angles are essential in the study of any geometric shape.
In this article, you will learn the angles of a triangle and how to find the unknown angles of a triangle when you only know some of the angles.
An angle of a triangle is the space formed between the two lengths of the sides of the triangle. A triangle contains interior angles and exterior angles. Interior angles are the three angles that lie inside a triangle. Exterior angles are formed when the sides of a triangle are extended to infinity.
Therefore, exterior angles are formed outside the triangle between one side of the triangle and the extended side. Every exterior angle is adjacent to an interior angle. Adjacent angles are angles with a common vertex and side.
Given:
The second angle in a triangle is five times as large as the first
The third angle is two-thirds as large as the first
To find:
Angles of the triangle?
Solution:
Let the first angle be x
The second angle be y
The third angle be z
According to the question:
We know that sum of all the angles of a triangle is 180°
Hence
x+y+z=180°
x+5x+(2/3)x=180°
20x/3=180°
x=27°
Therefore,
x=27°
y=5*27=135°
z=(2/3)*27=18°
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