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Difficulty: 3/102024 IOQM 2024 (Q4)

Let ABCD be quadrilateral with ∠ADC = 70°, ∠ACD = 70°, ∠ACB = 10° and ∠BAD = 110° . The measure of ∠CAB (in degrees) is:

Guide / Hint

Hint 1: Start by analyzing the initial conditions and setting up the basic equations. 70 + 70 + DAC = 180.

Hint 2: Look for algebraic properties, symmetry, or geometric theorems to simplify. => DAC = 40.

Hint 3: Proceed with the final algebraic steps to solve the system. Now DAC + CAB solve for the final value.

Solution

Step 1: 70° + 70° + ∠DAC = 180°

Step 2: => ∠DAC = 40°

Step 3: Now ∠DAC + ∠CAB = 110°

Step 4: => ∠CAB = 110° − 40°

Step 5: x z z x y zz x

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    2024 IOQM 2024 Q4 - Olympiad Math Olympiad Question | Leminno