In the figure below, ∠ACD = ∠BCE. How much is each

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Solution

From the figure, we can observe that ∠ACD and ∠DCB make a linear pair.

We know that the angles in a linear pair are supplementary.

∴ ∠ACD + ∠DCB = 180°

⇒ ∠ACD + (∠DCE + ∠ECB) = 180°

Given ∠ACD = ∠ECB and ∠DCE = 30°

⇒ ∠ACD + 30° + ∠ACD = 180°

⇒ 2∠ACD + 30° = 180°

⇒ 2∠ACD = 180° − 30°

⇒ 2∠ACD = 150°

⇒ ∠ACD = 75°

Thus, ∠ACD = ∠ECB = 75°.

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