AB is DC parallel to . Identify two pairs of congruent angles and the number of degrees in each congruent angle.
A) FAB BAD ; both are 29°.
EDC CDA ; both are 29°.
B) FAB EDC ; both are 29°.
ADC BAD ; both are 151°.
C) CDA FAB ; both are 151°.
EDC BAD ; both are 151°.
D) ADC BAD ; both are 29°.
FAB EDC ; both are 151°.
Parallel to what? "AB is CD"?
it would help to proofread your questions before you post them.
The correct answer is option A.
In option A, the two pairs of congruent angles are:
1) ∠FAB and ∠BAD, both of which are 29°.
2) ∠EDC and ∠CDA, both of which are also 29°.
To identify the two pairs of congruent angles and the number of degrees in each congruent angle, we need to understand the properties of parallel lines and transversals.
When a transversal intersects two parallel lines, the corresponding angles, alternate interior angles, and alternate exterior angles formed are congruent.
In the given scenario, AB is parallel to DC. Let's analyze each option:
A) FAB BAD; both are 29°.
This option refers to the corresponding angles formed by the transversal AB. Since AB is parallel to DC, the corresponding angles FAB and BAD are congruent, and both measure 29°.
EDC CDA; both are 29°.
This option refers to the corresponding angles formed by the transversal DC. Since DC is parallel to AB, the corresponding angles EDC and CDA are congruent, also measuring 29°.
B) FAB EDC; both are 29°.
This option refers to the alternate interior angles formed by the transversal AB. Since AB is parallel to DC, the alternate interior angles FAB and EDC are congruent and measure 29°.
ADC BAD; both are 151°.
This option refers to the alternate interior angles formed by the transversal DC. However, the statement is incorrect. The alternate interior angles ADC and BAD are not congruent in this case.
C) CDA FAB; both are 151°.
This option refers to the alternate exterior angles formed by the transversal DC. Since DC is parallel to AB, the alternate exterior angles CDA and FAB are congruent, measuring 151°.
EDC BAD; both are 151°.
This option refers to the alternate exterior angles formed by the transversal AB. However, the statement is incorrect. The alternate exterior angles EDC and BAD are not congruent in this case.
D) ADC BAD; both are 29°.
This option refers to the alternate interior angles formed by the transversal DC. Since DC is parallel to AB, the alternate interior angles ADC and BAD are congruent, measuring 29°.
FAB EDC; both are 151°.
This option refers to the alternate interior angles formed by the transversal AB. However, the statement is incorrect. The alternate interior angles FAB and EDC are not congruent in this case.
Based on the analysis, the correct answer would be option A, where both pairs of congruent angles are FAB BAD and EDC CDA, both measuring 29°.