Question

7.

1. $(7x + 16)^circ$

$128^circ$

1. $27^circ$

$(8x + 9)^circ$

Explanation:

Question 7

Step1: Identify complementary angles

The two angles sum to $90^\circ$.

Step2: Set up the equation

$x + 63^\circ = 90^\circ$

Step3: Solve for $x$

$x = 90^\circ - 63^\circ$

Question 10

Step1: Identify vertical angles

Vertical angles are equal.

Step2: Set up the equation

$7x + 16 = 128$

Step3: Isolate the term with $x$

$7x = 128 - 16$

Step4: Solve for $x$

$x = \frac{112}{7}$

Question 12

Step1: Identify supplementary angles

The angles form a linear pair, sum to $180^\circ$.

Step2: Set up the equation

$8x + 9 + 27 = 180$

Step3: Simplify the left side

$8x + 36 = 180$

Step4: Isolate the term with $x$

$8x = 180 - 36$

Step5: Solve for $x$

$x = \frac{144}{8}$

Answer:

Question 7: $27^\circ$
Question 10: $16$
Question 12: $18$