Question

complementary & supplementary two statements were made about each pair of angles. using the shape tool, circle the incorrect statement and type the statement correctly in the white rectangle.
a. the value of x is 55.
b. the measure of the smaller angle is 55°.
the smaller angle is 35 degrees.
a. the value of x is 10.
b. the angles measure 60° and 120°.
the value of x is 20.
a. the value of x is 19.
b. the measure of the larger angle is 38°.
two angles are complementary. the first angle is 2x degrees and the second angle is (3x - 5) degrees.

Explanation:

Part A

Step1: Set up complementary angle equation

The angles sum to $90^\circ$, so:
$$x + (x - 20) = 90$$

Step2: Solve for $x$

Simplify and isolate $x$:
$$2x - 20 = 90 \implies 2x = 110 \implies x = 55$$

Step3: Find smaller angle

Calculate $x-20$:
$$55 - 20 = 35^\circ$$

Part B

Step1: Set up supplementary angle equation

The angles sum to $180^\circ$, so:
$$3x + 6x = 180$$

Step2: Solve for $x$

Simplify and isolate $x$:
$$9x = 180 \implies x = 20$$

Step3: Calculate angle measures

Find $3x$ and $6x$:
$$3(20)=60^\circ, \quad 6(20)=120^\circ$$

Part C

Step1: Set up complementary angle equation

The angles sum to $90^\circ$, so:
$$2x + (3x - 5) = 90$$

Step2: Solve for $x$

Simplify and isolate $x$:
$$5x - 5 = 90 \implies 5x = 95 \implies x = 19$$

Step3: Find angle measures

Calculate $2x$ and $3x-5$:
$$2(19)=38^\circ, \quad 3(19)-5=52^\circ$$

Answer:

Part A

• Incorrect statement: B. The measure of the smaller angle is $55^\circ$.
• Correct statement: The smaller angle is 35 degrees.

Part B

• Incorrect statement: A. The value of x is 10.
• Correct statement: The value of x is 20.

Part C

• Incorrect statement: B. The measure of the larger angle is $38^\circ$.
• Correct statement: The larger angle is 52 degrees.