Questions: The diagram shows a triangle. What is the value of w ? w=

Transcript text: The diagram shows a triangle. What is the value of $w$ ? \[ w= \]

Solution

Step 1: Identify the given angles

The triangle has two given angles: 30° and 42°.

Step 2: Use the Triangle Angle Sum Theorem

The sum of the angles in a triangle is always 180°. Therefore, we can set up the equation: \[ 30° + 42° + 2w = 180° \]

Step 3: Simplify the equation

Combine the known angles: \[ 72° + 2w = 180° \]

Step 4: Solve for $ w $

Subtract 72° from both sides of the equation: \[ 2w = 108° \] Divide both sides by 2: \[ w = 54° \]

\[ w = 54° \]

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