50+ exterior angle property worksheets for 9th Year on Quizizz ... - Free Printable

Here are the step-by-step solutions for the questions in the worksheet.

Question 1

Goal: Find the measure of angle $F$.

1. Identify the angles: We have a triangle with interior angles at $E$ ($62^\circ$) and $F$ (unknown, let's call it $x$). There is an exterior angle at vertex $D$ measuring $146^\circ$.
2. Apply the Exterior Angle Theorem: This rule states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
* Formula: $\text{Exterior Angle} = \text{Remote Interior}_1 + \text{Remote Interior}_2$
3. Set up the equation:
$$146^\circ = 62^\circ + x$$
4. Solve for $x$:
$$x = 146 - 62$$
$$x = 84$$

The measure of angle $F$ is $84^\circ$. This matches option B.

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Question 2

Goal: Identify the term that best describes angle $d$.

1. Analyze the position: Angle $d$ is formed by extending one side of the triangle. It sits outside the triangle, next to interior angle $c$.
2. Evaluate the options:
* Remote interior angle: These are the angles inside the triangle that are not touching the exterior angle (angles $a$ and $b$).
* Exterior angle: This is an angle formed by one side of a triangle and the extension of an adjacent side. This fits angle $d$ perfectly.
* Corresponding angle: This usually refers to angles formed when a line crosses parallel lines.
* Interior angle: These are angles inside the shape ($a$, $b$, and $c$).

Angle $d$ is an Exterior angle. This matches option B.

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Question 3

Goal: Find the measure of angle $b$.

1. Identify the angles: We have an exterior angle of $117^\circ$. The remote interior angles are $81^\circ$ and angle $b$.
2. Apply the Exterior Angle Theorem:
$$\text{Exterior Angle} = \text{Sum of Remote Interior Angles}$$
$$117^\circ = 81^\circ + b$$
3. Solve for $b$:
$$b = 117 - 81$$
$$b = 36$$

The measure of angle $b$ is $36^\circ$. This matches option B.

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Question 4

Goal: Find the measure of angle $S$ (labeled with a question mark).

1. Identify the angles: The exterior angle at vertex $T$ is $120^\circ$. The remote interior angles are angle $S$ (unknown) and angle $R$ ($60^\circ$).
2. Apply the Exterior Angle Theorem:
$$120^\circ = \angle S + 60^\circ$$
3. Solve for $\angle S$:
$$\angle S = 120 - 60$$
$$\angle S = 60$$

The measure of angle $S$ is $60^\circ$. This matches option A.

Looking at the answer choices provided at the bottom of Question 4:
* A) D
* B) B
* C) C
* D) A

Since the calculated answer corresponds to option A from the list ($60^\circ$), we must select the choice that points to "A". That is choice D.

Final Answer:
1. B
2. B
3. B
4. D