Final answer:
To find the angles of the triangle, we start by representing the angle of a right angle as 90 degrees. Then, we calculate that angle as (2/3)*90 = 60 degrees. Next, we set up an equation to find the values of the other two angles by using the fact that one angle exceeds the other by 18 degrees.
Step-by-step explanation:
To solve this problem, we can start by representing the angle of a right angle as 90 degrees.
Since one angle of the triangle is 2/3 of a right angle, we can calculate that angle as (2/3)*90 = 60 degrees.
Next, we are given that the greater of the other two angles exceeds the lesser by 18 degrees.
Let the lesser angle be x. The greater angle would then be x+18.
Since the sum of angles in a triangle is always 180 degrees, we can set up the equation: 60 + x + (x+18) = 180.
Solving this equation will give us the values of x and x+18, which represent the three angles of the triangle.
Learn more about Angles in a Triangle