ABCD is a rhombus. The diagonals AC and BD intersect at O. Angle CAB = 35 degrees. Find angle ADB.
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Worked Solution
Step 1: Use the property that a diagonal of a rhombus bisects the vertex angle.
Diagonal AC bisects angle DAB, so angle DAB = 2 x angle CAB = 2 x 35 = 70 degrees.
Step 2: Use the property that the diagonals of a rhombus are perpendicular.
Angle AOB = 90 degrees.
Step 3: Find angle ABO in triangle AOB.
In triangle AOB: angle OAB + angle AOB + angle ABO = 180
35 + 90 + angle ABO = 180
Angle ABO = 55 degrees
Step 4: Use the property that all sides of a rhombus are equal.
AB = AD, so triangle ABD is isosceles.
Therefore angle ADB = angle ABD = angle ABO = 55 degrees.
Answer: Angle ADB = 55 degrees.
Correct answer: 55°
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