Question

Find the measure of angle a​

Answer 1

`\angle A = 40^o`

Explanation:

Notice that angle A is identified with the algebraic expression "7 + 3 x", while the other acute angle is identified with the expression "5 x - 5"

We know that the third angle is a right angle (90 degrees),

and also that the sum of the internal angles in a triangle must give 180 degrees, so we have:

`\angle A + \angle B+ 90^o = 180^o\\(7+3\,x)+(5\,x-5)=180^o-90^o\\7+3\,x+5\,x-5=90^o\\8\,x+2 = 90^o\\8\,x=88^o\\x=11^o`

Now that we know x, we can give the answer for what angle A is:

`\angle A= 7^o+3\,x\\\angle A =7^o+3\,(11^o)\\\angle A = 7^o+33^o\\\angle A = 40^o`