in a right angled triangle abc . angle A is equals to 90. angle b is equals to 2 / 3 of the Other angles c. find the measure of the angle B and angle C
In a triangle, the sum of the three angles is always equal to 180 degrees. Therefore, we have:
**Angle A + Angle B + Angle C = 180 degrees**
Since Angle A is a right angle, its measure is 90 degrees. We are also given that Angle B is equal to 2/3 of the remaining angle (Angle C). Let's represent Angle C as "x".
Therefore, we can rewrite the equation as:
**90 degrees + (2/3)x + x = 180 degrees**
Combining like terms:
**5/3 x + 90 degrees = 180 degrees**
Subtracting 90 degrees from both sides:
**5/3 x = 90 degrees**
Multiplying both sides by 3/5:
**x = 54 degrees**
Now that we know Angle C is 54 degrees, we can find Angle B using the formula:
**Angle B = (2/3) * Angle C**
Substituting the value of Angle C:
**Angle B = (2/3) * 54 degrees = 36 degrees**
Therefore, the measure of **Angle B is 36 degrees** and the measure of **Angle C is 54 degrees**.
Answers & Comments
Answer:
Step-by-step explanation:
In a triangle, the sum of the three angles is always equal to 180 degrees. Therefore, we have:
**Angle A + Angle B + Angle C = 180 degrees**
Since Angle A is a right angle, its measure is 90 degrees. We are also given that Angle B is equal to 2/3 of the remaining angle (Angle C). Let's represent Angle C as "x".
Therefore, we can rewrite the equation as:
**90 degrees + (2/3)x + x = 180 degrees**
Combining like terms:
**5/3 x + 90 degrees = 180 degrees**
Subtracting 90 degrees from both sides:
**5/3 x = 90 degrees**
Multiplying both sides by 3/5:
**x = 54 degrees**
Now that we know Angle C is 54 degrees, we can find Angle B using the formula:
**Angle B = (2/3) * Angle C**
Substituting the value of Angle C:
**Angle B = (2/3) * 54 degrees = 36 degrees**
Therefore, the measure of **Angle B is 36 degrees** and the measure of **Angle C is 54 degrees**.