Question

ABCD is a kite. If m∠BAD = 34° and m∠BCD = 60°, find m∠ABC.

Answer 1

In a kite, the two pairs of angles formed by the intersecting diagonals are congruent. By using this property and the fact that the sum of the angles in a triangle is 180°, we can find that m∠ABC is 86°.

Step-by-step explanation:

We know that in a kite, the two pairs of angles formed by the intersecting diagonals are congruent. Therefore, since m∠BAD = 34°, we can conclude that m∠BCA = 34°. Similarly, since m∠BCD = 60°, we can conclude that m∠BAC = 60°.

To find m∠ABC, we use the fact that the sum of the angles in a triangle is 180°. So, m∠ABC + m∠BAC + m∠BCA = 180°. Substituting the known values, we have m∠ABC + 60° + 34° = 180°.

Simplifying the equation, we get m∠ABC = 86°.