Given:
and
are complementary angles.
To find:
The measure of .
Solution:
According to the definition of the complimentary angles, the sum of two complementary angles is always 90 degree.
It is given that, and
are complementary angles. So,
Therefore, the measure of is 58°.
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Refer to the attached figure.
There are a couple of ways you can go at this. One is to show the sums of the marked angles are the same, hence ∠B ≅ ∠D. Instead, we're going to show that ΔABD ≅ ΔCDB, hence ∠A ≅ ∠C.
1. AB║DC and BC║AD . . . . given
2. BD is a transversal to both AB║DC and BC║AD . . . . given
3. ∠CBD ≅ ∠ADB . . . . alternate interior angles where a transversal crosses parallel lines are congruent
4. ∠CDB ≅ ∠ABD . . . . alternate interior angles where a transversal crosses parallel lines are congruent
5. BD ≅ BD . . . . reflexive property of congruence
6. ΔABD ≅ ΔCDB . . . . ASA postulate
7. ∠A ≅ ∠C . . . . CPCTC
∠A and ∠C are opposite angles of parallelogram ABCD, so we have shown what you want to have shown.
