In the figure shown, 1∥2. If m∠8=49°, determine the measures of the other seven angles in the figure.
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To determine the measures of the other seven angles in the figure, we'll need to use the properties of parallel lines and transversals. Here's how you can approach this problem step by step:
Step 1: Identify corresponding angles.
Since line 1 is parallel to line 2, any pair of angles that are on the same side of the transversal (line 3) and on the same side of the parallel lines will be corresponding angles. Corresponding angles have equal measures.
Step 2: Identify alternate interior angles.
When a transversal intersects two parallel lines, any pair of angles that are on opposite sides of the transversal, between the parallel lines, will be alternate interior angles. Alternate interior angles have equal measures.
Step 3: Use the given information.
In the figure, it is given that m∠8 = 49°. We can use this information along with the properties of corresponding angles and alternate interior angles to determine the measures of the other angles.
Now, let's find the measures of the angles:
1. ∠8: The measure is given as 49°.
2. ∠3: ∠3 is corresponding to ∠8, so its measure will also be 49°.
3. ∠7: ∠7 is alternate interior to ∠8, so its measure will also be 49°.
4. ∠4: ∠4 is corresponding to ∠7, so its measure will also be 49°.
5. ∠6: ∠6 is alternate interior to ∠7, so its measure will also be 49°.
6. ∠1: ∠1 is corresponding to ∠6, so its measure will also be 49°.
7. ∠2: ∠2 is alternate interior to ∠6, so its measure will also be 49°.
Therefore, the measures of the other seven angles in the figure are:
1. ∠8 = 49°
2. ∠3 = 49°
3. ∠7 = 49°
4. ∠4 = 49°
5. ∠6 = 49°
6. ∠1 = 49°
7. ∠2 = 49°
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