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Chapter 3: Q6. (page 111)

In the diagram abover鈭�s.

Solve for x:role="math" localid="1650007841155" m鈭�2=70 andm鈭�8=6x-2.

Short Answer

Expert verified

The value ofx is 12.

Step by step solution

01

Step 1. Highlight and in the given diagram.

02

Step 2. Apply the property of parallel lines.

If two parallel lines are intersected by a transversal then the alternate interior angles are congruent.

03

Step 3. Description of step.

From the given figure it can be observed thatr鈭�s andt is transversal then by the definition of alternate interior angles,鈭�2 and鈭�8 are alternate interior angles and by property of parallel lines, 鈭�2鈮�鈭�8.

Therefore, m鈭�2=m鈭�8.

04

Step 4. Description of step.

Substitute70 form鈭�2 and6x鈭�2 form鈭�8 intom鈭�2=m鈭�8 and simplify.

70=6x鈭�272=6xx=726=12

Therefore, the value ofx is 12.

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