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In a parallelogram KITE, angleKIT = 75^(...

In a parallelogram KITE, `angleKIT = 75^(@), KA bot IT`, KA and El intersect at B where A is a point on IT. If EB = 2KI, then the measure of `angleKBE` is

A

`62^(@)`

B

`65^(@)`

C

`68^(@)`

D

`70^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the measure of angle KBE in the parallelogram KITE, given that angle KIT = 75° and KA is perpendicular to IT. We also know that EB = 2KI. ### Step-by-Step Solution: 1. **Understanding the Parallelogram and Given Angles**: - We have a parallelogram KITE where angle KIT = 75°. - Since K is perpendicular to IT, angle KAI = 90°. 2. **Finding Angle IKA**: - In triangle KAI, the sum of angles is 180°. - Therefore, angle IKA = 180° - angle KIT - angle KAI = 180° - 75° - 90° = 15°. 3. **Identifying Parallel Lines**: - Since KITE is a parallelogram, we know that sides KE and IT are parallel. - This means that angle KBE will be equal to angle IKA due to alternate interior angles. 4. **Using the Given Information about EB**: - We know that EB = 2KI. However, this information is not directly needed to find angle KBE since we already established the relationship between the angles. 5. **Calculating Angle KBE**: - Since angle KBE is equal to angle IKA, we have: - angle KBE = angle IKA = 15°. ### Final Answer: The measure of angle KBE is **15°**. ---
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