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In the diagram, OBbisects AOCand ECOD.

Find the value of x.

m1=2x, m2=6x+2.

Short Answer

Expert verified

The value of xis 11.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Write the relation between the angles ∠1 and ∠2.

As, ECOD, therefore the lines EC and OD are perpendicular lines.

Therefore, by using the definition of perpendicular lines it can be said that the measures of the angle DOEis 90°.

That implies, mDOE=90°.

Now, by using the angle addition postulate it can be said that mDOE=m1+m2.

Therefore, the relation between the angles ∠1 and ∠2 is:

mDOE=m1+m2

90=m1+m2

03

Step 3. Find the value of x.

As, m1+m2=90°, m1=2xand m2=6x+2.

Therefore, the value of x is given by:

role="math" localid="1646589364482" m1+m2=90°

2x+6x+2=90°

8x+2=90°

8x=90°2

8x=88°

x=888

x=11

Therefore, the value of x is 11.

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