Math / Geometry

Questionfintre given figure $\overrightarrow{A B}, \overrightarrow{C D} . \overrightarrow{P Q}$ and $\overrightarrow{R S}$ are two transversals. Evaluate the angles s. $y$ and $=$

Studdy Solution

STEP 1

1. The lines $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are parallel.
2. The angles $x$ and $y$ are alternate interior angles.
3. The angle $z$ is a corresponding angle.
4. The transversal $\overrightarrow{PQ}$ intersects the parallel lines creating the angle $\angle PIQ = 60^\circ$ .
5. The transversal $\overrightarrow{RS}$ intersects the parallel lines creating the angle $\angle IRS = 75^\circ$ .

STEP 2

1. Use properties of parallel lines and transversals to find angle $x$ .
2. Use properties of parallel lines and transversals to find angle $y$ .
3. Use properties of parallel lines and transversals to find angle $z$ .

STEP 3

Since $x$ is an alternate interior angle to $\angle PIQ$ and the lines are parallel, we have:
$x = \angle PIQ = 60^\circ$

STEP 4

Since $y$ is an alternate interior angle to $\angle IRS$ and the lines are parallel, we have:
$y = \angle IRS = 75^\circ$

STEP 5

Since $z$ is a corresponding angle to $\angle PIQ$ and the lines are parallel, we have:
$z = \angle PIQ = 60^\circ$
The evaluated angles are:
$x = 60^\circ, \quad y = 75^\circ, \quad z = 60^\circ$

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