Final Answer:
The measure of ∠a is 5x - 5∘, and the measure of ∠b is 3x + 13∘.
Step-by-step explanation:
To find the measure of each angle, we need to substitute the given expressions into the formula for the area of a triangle, which is given by:
Area = (base × height) / 2
Since the base and height of the triangle are given as 3x and 5x - 5, respectively, we can substitute these values into the formula to get:
Area = (3x × (5x - 5)) / 2
Expanding the product and simplifying the expression, we get:
Area = 3x^2 - 10x + 5
Now, we are asked to find the measure of each angle. To do this, we can use the fact that the sum of the measures of the interior angles of a triangle is 180 degrees. So, we can set up the following equation:
∠a + ∠b + ∠c = 180
where ∠c is the measure of the third angle of the triangle, which is not given.
Substituting the expressions for ∠a and ∠b into the equation, we get:
5x - 5∘ + 3x + 13∘ + ∠c = 180
Simplifying the equation, we get:
8x + ∠c = 180
Now, we can solve for ∠c by subtracting 8x from both sides of the equation:
∠c = 180 - 8x
Since ∠c is the measure of the third angle of the triangle, we know that it must be equal to 180 degrees minus the sum of the measures of ∠a and ∠b. So, we can substitute the expressions for ∠a and ∠b into the equation to get:
∠c = 180 - (5x - 5∘ + 3x + 13∘)
Simplifying the expression, we get:
∠c = 180 - 8x
Therefore, the measure of ∠a is 5x - 5∘, and the measure of ∠b is 3x + 13∘.