Since < ABD is a right triangle (with a measure of 90 °), we can establish the formula to solve for the value of x:
Let < BAC = m < 1 = (15x - 2)°
< CAD = m < 2 = (7x + 4)°
Use the formula:
m < 1 + m < 2 = 90°
Substitute the values of m < 1 and 2:
15x - 2 + 7x + 4 = 90°
Combine like terms:
22x + 2 = 90°
Subtract 2 from both sides:
22x + 2 - 2 = 90° - 2
22x = 88°
Divide both sides by 22:
22x/22 = 88/22
x = 4
Now that we have the value of x, we can plug this value into the given angles:
< BAC = m < 1 = (15x - 2)° = 15(4) - 2 = 58°
< CAD = m < 2 = (7x + 4)° = 7(4) + 4 = 32°
m < 1 + m < 2 = 90°
58° + 32° = 90°
90° = 90° (true statement).
Therefore, (15x - 2)° = 58° and (7x + 4)° = 32°.
Please mark my answers as the Brainliest if you find my explanations helpful :)
