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Let's work through it step-by-step. We are given: Triangle ABC is isosceles (with AB = AC, since angle BAC is given). AE and AF are straight lines. ∠EBD = 65° ∠BAC = 80° D is the intersection of the bisectors of ∠EBC and ∠FCB. We are to find ∠BDC. --- Step 1: Triangle ABC Since triangle ABC is isosceles with ∠BAC = 80°, and the equal sides are AB = AC, the base angles ∠ABC and ∠ACB are equal. So, we calculate: \angle ABC = \angle ACB = \frac{180° - 80°}{2} = 50° --- Step 2: Using ∠EBD = 65° From the diagram description, EBD is part of angle EBC. So: ∠EBC = ∠EBD + ∠CBD We're told ∠EBD = 65° D lies on the bisector of ∠EBC, so ∠EBD = ∠CBD Thus, both are 65°, meaning: \angle EBC = \angle EBD + \angle CBD = 65° + 65° = 130° But earlier we found: \angle ABC = 50° That suggests EBC is an exterior angle at B, formed when AE extends past AB (same with FCB being an exterior angle at C). --- Step 3: Find angles EBC and FCB Since ∠ABC = 50°, its exterior angle ∠EBC = 180° - 50° = 130° ...
Note
Crop rotation is a farming practice that involves rotating different crops on the same land to maintain soil fertility, reduce pests and diseases, and increase crop yields. Here are some general rules governing crop rotation: Basic Principles 1. *Rotate crops with different nutrient requirements*: Alternate between crops that deplete soil nutrients and those that replenish them. 2. *Rotate crops with different growth habits*: Alternate between crops with different growth patterns, such as legumes and cereals. 3. *Avoid consecutive planting of crops susceptible to the same pests or diseases*: Rotate crops to break disease and pest cycles. Benefits 1. *Improved soil fertility*: Crop rotation can increase soil nutrient availability and structure. 2. *Pest and disease management*: Rotation can reduce the buildup of pests and diseases. 3. *Increased crop yields*: Crop rotation can lead to more efficient use of resources and improved crop productivity. Planning a Crop Rotation 1. *Consi...
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