Questions: 159° x 85° y

Transcript text: 159° $x$ 85° $y$

Solution

Solution Steps

Step 1: Identify the relationship between angles

In the given diagram, we have a straight line and a triangle. The angle on the straight line (159°) and the adjacent angle (x) form a linear pair, which means they add up to 180°.

Step 2: Calculate angle x

Using the linear pair relationship: \[ x + 159° = 180° \] \[ x = 180° - 159° \] \[ x = 21° \]

Step 3: Use the triangle angle sum property

In the triangle, the sum of the interior angles is 180°. We know two of the angles: 85° and y. The third angle is x, which we calculated as 21°.

Step 4: Calculate angle y

Using the triangle angle sum property: \[ 21° + 85° + y = 180° \] \[ 106° + y = 180° \] \[ y = 180° - 106° \] \[ y = 74° \]

Final Answer

\[ x = 21° \] \[ y = 74° \]

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