Questions: What is the value of t? t= 0

What is the value of t? t= 0
Transcript text: What is the value of $t$ ? \[ t= \] $\square$ 0
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Solution

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Solution Steps

Step 1: Identify the Exterior Angle Theorem

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Step 2: Set Up the Equation

Given:

  • One exterior angle is \(35^\circ\).
  • The two non-adjacent interior angles are \(t^\circ\) and \(t + 10^\circ\).

According to the Exterior Angle Theorem: \[ 35^\circ = t^\circ + (t + 10^\circ) \]

Step 3: Solve for \(t\)

Combine like terms: \[ 35^\circ = t + t + 10 \] \[ 35^\circ = 2t + 10 \]

Subtract 10 from both sides: \[ 25^\circ = 2t \]

Divide by 2: \[ t = 12.5^\circ \]

Final Answer

\[ t = 12.5^\circ \]

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