Questions: Use the triangle

Transcript text: 9) Use the triangle

Solution

Solution Steps

Step 1: Determine the missing angle in the first triangle

In a triangle, the sum of the interior angles is always 180°. Given two angles are 24° and 123°, we can find the missing angle by subtracting the sum of these two angles from 180°.

\[ 180° - (24° + 123°) = 180° - 147° = 33° \]

Final Answer

The missing angle in the first triangle is 33°.

Step 2: Set up the equation for the second triangle

In the second triangle, the sum of the interior angles is also 180°. Given two angles are 50° and 55°, and the third angle is \( x + 86 \), we can set up the equation:

\[ 50° + 55° + (x + 86)° = 180° \]

Step 3: Solve for \( x \)

Combine the known angles and solve for \( x \):

\[ 105° + (x + 86)° = 180° \] \[ x + 191° = 180° \] \[ x = 180° - 191° \] \[ x = -11° \]

Final Answer

The value of \( x \) in the second triangle is -11°.

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