Question

12
the angles represented by the expressions $(2x + 46)^{circ}$ and $(3x - 6)^{circ}$ are complementary angles. find the measure of the larger angle.

write the equation: $2x + 46 + 3x - 6 = 90$

larger angle: $square^{circ}$

Explanation:

Step1: Combine like terms

$2x + 3x + 46 - 6 = 90$
$5x + 40 = 90$

Step2: Isolate the term with $x$

$5x = 90 - 40$
$5x = 50$

Step3: Solve for $x$

$x = \frac{50}{5}$
$x = 10$

Step4: Calculate both angles

First angle: $2(10) + 46 = 20 + 46 = 66^\circ$
Second angle: $3(10) - 6 = 30 - 6 = 24^\circ$

Step5: Identify the larger angle

Compare $66^\circ$ and $24^\circ$

Answer:

$66$