Two adjacent angles form a resulting angle with measure 90° . (x+4)° and (3x+2)° . Solve for x . What are the two unknown angles’ measurements?

1 answer

Two adjacent angles form a straight angle which has a measure of 180°. Since the resulting angle formed by the two adjacent angles is 90°, it means that the two adjacent angles are complementary. Therefore, we can set up the equation:

(x+4) + (3x+2) = 90

Simplifying this equation, we combine like terms:

4x + 6 = 90

Next, we isolate the variable:

4x = 90 - 6
4x = 84

Dividing both sides by 4:

x = 84/4
x = 21

Now, we substitute the value of x back into the expressions for the two unknown angles:

Angle 1: (21+4)° = 25°
Angle 2: (3(21)+2)° = 65°

Therefore, the two unknown angles’ measurements are 25° and 65°.