In triangle abc, ab=cb, m∠abc=4x-3 and m∠cab=x-3. what is m∠abc?
a. 28.5
b. 31.5
c. 63
d. 34.5
To find the measure of angle ABC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We are given that AB = CB, which means that angles ABC and ACB are congruent. Let's call each of these angles y.
So, we have the following equation: 4x - 3 + x - 3 + y = 180.
Simplifying this equation, we get: 5x - 6 + y = 180.
We know from the information given that y = 4x - 3, so we can substitute this into the equation: 5x - 6 + 4x - 3 = 180.
Combining like terms, we get: 9x - 9 = 180.
Adding 9 to both sides, we get: 9x = 189.
Dividing both sides by 9, we find: x = 21.
Now, we can substitute x = 21 into the equation y = 4x - 3: y = 4(21) - 3 = 84 - 3 = 81.
Since angles ABC and ACB are congruent, angle ABC is also 81 degrees.
Therefore, the answer is d. 34.5 degrees.