Question

find the measure of each marked angle. (7x - 27)° = □° (type integers or decimals) (6x)° = □°

Explanation:

Step1: Set up equation

Since the two angles are complementary (sum to 90°), we have the equation $(7x - 27)+6x=90$.

Step2: Combine like - terms

$7x+6x-27 = 90$, which simplifies to $13x-27 = 90$.

Step3: Add 27 to both sides

$13x-27 + 27=90 + 27$, so $13x=117$.

Step4: Solve for x

$x=\frac{117}{13}=9$.

Step5: Find the measure of the first angle

Substitute $x = 9$ into $7x-27$. We get $7\times9-27=63 - 27=36$.

Step6: Find the measure of the second angle

Substitute $x = 9$ into $6x$. We get $6\times9 = 54$.

Answer:

$(7x - 27)^{\circ}=36^{\circ}$
$(6x)^{\circ}=54^{\circ}$