B: B||D

C: C||E

D: C||D

E: D||F

F: E||F

Asked
1 year ago

Viewed
411440 times

**Answer:**

**Options A, C and D**

**Step-by-step explanation:**

**Option A**

Angle p = 180° - 89.5° = 90.5° [Linear pair of angles]

If b║f and line a is a transversal line,

m∠p = 90.5° [Alternate exterior angles]

**True**

**Option B**

If B║D and line a is a transversal,

m∠q = 89.5° [vertically opposite angles]

∠q + 89.5° = 89.5° + 89.5° = 179°

But angles q and angle with measure 89.5° are the consecutive interior angles and their sum should be 180°.

So the given statement is **False.**

**Option C**

c║e

Since, m∠r = 91.5° [Vertically opposite angle]

And m∠r + 89.5° = 180° [Consecutive interior angles]

**True.**

**Option D**

c║d

Since, ∠r and ∠q are consecutive interior angles,

m∠r + m∠q = 180°

91.5° + 89.5° = 180°

**True**

**Option E.**

d║f

m∠s = 90.5°[Vertically opposite angles]

Since, ∠s and angle with measure 89.5° are the alternate interior angles,

So measure of angle s should be 89.5°.

Therefore, d║f is **False.**

**Option F.**

If e║f, angles with measures 89.5° and 90.5° should be equal.

But measures of both are different.

Therefore, e║f is **False.**

**Options A, C and D are the correct options.**

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