Mathematics
Grade9
Easy

Question

Given that m∠FHE = m∠BHG = m∠AHF = 90 in the below diagram, answer the following:
If m∠6 = 27, then m∠1 =?

  1. 27
  2. 30
  3. 37
  4. 47

hintHint:

They are always equal to each other. In other words, whenever two lines cross or intersect each other, 4 angles are formed. We can observe that two angles that are opposite to each other are equal and they are called vertical angles.

The correct answer is: 27


    According to the congruent complements theorem, if two angles are complementary to the same angle (or to congruent angles), then they are congruent.
    m∠6 and ∠7 are complementary and m∠7, and m∠1 are complementary, so m∠1 and m∠6 are congruent angles.
    m∠1 = 27.
    Hence, the correct option is A.

    Vertical angles are formed when two lines meet each other at a point.

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