In this triangle, angle BAC is 25% of the size of angle ABC. Angle ACB is 90 degrees less than triangle ABC.
What is the Size of angle ABC?
x + x/4 +(x-90) = 180
2.25 x = 270
x = 120
To find the size of angle ABC, we need to follow these steps:
1. Let's assume the size of angle ABC is represented by 'x' degrees.
2. According to the problem, angle BAC is 25% of the size of angle ABC. This means angle BAC is (25/100) * x = 0.25x degrees.
3. Angle ACB is given to be 90 degrees less than angle ABC. So ACB = x - 90 degrees.
4. In any triangle, the sum of all angles is 180 degrees. Therefore, we can write the equation: BAC + ABC + ACB = 180.
5. Substitute the values we obtained in steps 2 and 3 into the equation from step 4: 0.25x + x + (x - 90) = 180.
6. Simplify the equation: 0.25x + x + x - 90 = 180.
7. Combine like terms: 2.25x - 90 = 180.
8. Add 90 to both sides: 2.25x = 270.
9. Divide both sides by 2.25: x = 120.
Therefore, the size of angle ABC is 120 degrees.