Question

find the value of x.

9)
10)
11)
12)
13)
14)
15)
16)

Explanation:

Identify geometric relationships

We analyze each numbered problem from the image to find the value of \(x\).

• Question 9: The two adjacent angles form a right angle, indicated by the square symbol. Thus, they are Complementary Angles.

$$ x + 23 = 90 \implies x = 67 $$

• Question 10: The two adjacent angles form a right angle, indicated by the square symbol. Thus, they are Complementary Angles.

$$ x + 37 = 90 \implies x = 53 $$

• Question 11: The two angles are opposite each other at an intersection of two lines. By the Vertical Angles Theorem, they are equal.

$$ 4x + 1 = x + 16 \implies 3x = 15 \implies x = 5 $$

• Question 12: The two adjacent angles lie on a straight line. By the Linear Pair Postulate, they are supplementary.

$$ (17 + 2x) + (6x + 3) = 180 \implies 8x + 20 = 180 \implies 8x = 160 \implies x = 20 $$

• Question 13: The two adjacent angles form a right angle, indicated by the square symbol. Thus, they are Complementary Angles.

$$ (x + 15) + 50 = 90 \implies x + 65 = 90 \implies x = 25 $$

• Question 14: The two adjacent angles form a right angle, indicated by the square symbol. Thus, they are Complementary Angles.

$$ (x + 2) + 66 = 90 \implies x + 68 = 90 \implies x = 22 $$

• Question 15: The two angles are opposite each other at an intersection of two lines. By the Vertical Angles Theorem, they are equal.

$$ 4x + 9 = 95 \implies 4x = 86 \implies x = 21.5 $$

• Question 16: The two adjacent angles lie on a straight line. By the Linear Pair Postulate, they are supplementary.

$$ (6x + 2) + (x + 3) = 180 \implies 7x + 5 = 180 \implies 7x = 175 \implies x = 25 $$

Answer:

No.	Problem Type	Answer
10	Complementary Angles	\(x = 53\)
11	Vertical Angles	\(x = 5\)
12	Linear Pair	\(x = 20\)
13	Complementary Angles	\(x = 25\)
14	Complementary Angles	\(x = 22\)
15	Vertical Angles	\(x = 21.5\)
16	Linear Pair	\(x = 25\)