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Find Measure of angle

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°.

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