Wo angies in an equilateral triangie are \( (a+b) \) and \( (2 a-10 b) \) degrees Find the values of \( a \) and \( b \).

To solve for \( a \) and \( b \) in an equilateral triangle where the angles are given by \( (a + b) \) and \( (2a - 10b) \) degrees, follow these steps: 1. **Understanding an Equilateral Triangle:** - In an **equilateral triangle**, all three angles are equal. - Each angle in an equilateral triangle is **60 degrees**. 2. **Setting Up the Equations:** - Since all angles are equal, we can set: \[ a + b = 60^\circ \] \[ 2a - 10b = 60^\circ \] 3. **Solving the Equations:** - From the first equation: \[ a = 60^\circ - b \] - Substitute \( a \) from the first equation into the second equation: \[ 2(60 - b) - 10b = 60 \] \[ 120 - 2b - 10b = 60 \] \[ 120 - 12b = 60 \] \[ -12b = -60 \] \[ b = 5^\circ \] - Substitute \( b = 5^\circ \) back into the first equation to find \( a \): \[ a = 60^\circ - 5^\circ = 55^\circ \] 4. **Final Solution:** \[ a = 55^\circ \quad \text{and} \quad b = 5^\circ \] **Answer:** After simplifying, a is 55 degrees and b is 5 degrees.