In parallelogram ABCD below, the measure of ∠BCD is 98° and the measure of ∠CDB is 38°. What is the measure of ∠BDA ?
Question
In parallelogram ABCD below, the measure of ∠BCD is 98° and the measure of ∠CDB is 38°. What is the measure of ∠BDA ?
Solution
In a parallelogram, opposite angles are equal and adjacent angles are supplementary.
- Since ∠BCD is 98°, ∠DAB (opposite angle) is also 98°.
- ∠CDB is 38°, so ∠BDA (adjacent angle) is supplementary to ∠CDB.
To find the measure of ∠BDA, subtract the measure of ∠CDB from 180° (since supplementary angles add up to 180°).
So, ∠BDA = 180° - 38° = 142°.
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