Angle a equals 4x-6 angle b equals 3x-2 and angle c equals 3x-2. Use triangle sum theorem to find the measure of triangle a
The triangle sum theorem states that the sum of the measures of the angles in a triangle is always 180 degrees.
In this case, we have angle a, angle b, and angle c.
So, we can write the equation: angle a + angle b + angle c = 180.
Substituting the given measures of angles a, b, and c, we have:
(4x-6) + (3x-2) + (3x-2) = 180.
Combining like terms, we get:
10x - 10 = 180.
Adding 10 to both sides, we have:
10x = 190.
Dividing both sides by 10, we get:
x = 19.
Now we can substitute the value of x back into the expressions for angles a, b, and c to find their measures.
angle a = 4x - 6 = 4(19) - 6 = 76 - 6 = 70 degrees.
Therefore, the measure of triangle a is 70 degrees.