Questions: A side of the triangle below has been extended to form an exterior angle of 126°. Find the value of x.

A side of the triangle below has been extended to form an exterior angle of 126°. Find the value of x.
Transcript text: A side of the triangle below has been extended to form an exterior angle of $126^{\circ}$. Find the value of $x$.
failed

Solution

failed
failed

Solution Steps

Step 1: Understand the Problem

We need to find the value of \( x \) in the given triangle where one side has been extended to form an exterior angle of \( 126^\circ \).

Step 2: Use the Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the exterior angle is \( 126^\circ \), and the two non-adjacent interior angles are \( 16^\circ \) and \( x \).

Step 3: Set Up the Equation

According to the Exterior Angle Theorem: \[ 126^\circ = 16^\circ + x \]

Step 4: Solve for \( x \)

Subtract \( 16^\circ \) from both sides of the equation: \[ x = 126^\circ - 16^\circ \] \[ x = 110^\circ \]

Final Answer

\[ x = 110^\circ \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
13) sec -3 π 14) cot 13π/6 15) tan 7π/2 16) cot -π
failedAnswered
Translate the argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. You got an A in Math, or I am happy. Today I'm happy. Therefore, Today you did not get an A in Math. (i) Click the icon to view tables of standard valid and invalid forms of arguments. Let p represent "Today you got an A in Math," and let q represent "Today I'm happy." Select the correct choice below and fill in the answer box with the symbolic form of the argument. (Type the terms of your expression in the same order as they appear in the original expression.) A. The argument is invalid. In symbolic form the argument is B. The argument is valid. In symbolic form the argument is
failedAnswered
Si una circunferencia es tangente a los ejes de coordenadas en los puntos (0,-π) y (-π, 0), el centro de la circunferencia es A) (π, π) B) (π,-π) C) (-π,-π) D) (-π, π)
failedAnswered
A nurse is preparing to administer medications to a client who is not wearing an identification bracelet. Which of the following actions should the nurse take before administering the medications? Verify the client's identity using their diagnosis. Use one identifier to confirm the client's identity. Use the client's room number to identify the client. Have the client confirm their name and date of birth.
failedAnswered
Compare the graph of the function, f(x)=x, with the graph of the function, g(x)=x/3. For each point, (a, b), on f(x), there is a corresponding point, (3a, b), on g(x). The graph of g(x) is a horizontal stretch of magnitude 3 applied to the graph of f(x). For each point, (a, b), on f(x), there is a corresponding point, (1/3a, b), on g(x). The graph of g(x) is a horizontal shrink of magnitude 3 applied to the graph of f(x). For each point, (a, b), on f(x), there is a corresponding point, (a, 1/3b), on g(x). The graph of g(x) is a vertical shrink of magnitude 3 applied to the graph of f(x).