Question

0. In the given figure, if BEC = 120°, DCE = 25°, then find BAC.
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Answer 1

Answer:

is given on the above picture

Step-by-step explanation:

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Answer 2

Given:

BEC = 120°

DCE = 25°

To Find:

BAC

Solution:

∠BAC = ∠CDE [Angles in the segment of the circle] ..(i)

∠BEC is the exterior angle of the triangle.

In ΔCDE,

⇒ ∠CEB = ∠CDE + ∠DCE [Exterior angles of Δ]

⇒ 120° = ∠CDE + 25° [the measures of ∠BEC and ∠DCE is given]

⇒ ∠CDE = 120°-25°

⇒ ∠CDE = 95°

As we know, ∠BAC = ∠CDE because of angles in the segment of the circle.

Thus, ∠BAC = 95° [Using (i)]

Therefore, the measure of ∠BAC = 95°