What is the value of z in the diagram?

Mathematics
What is the value of z in the diagram?

ScanSolve AI Answer

Answer

30∘30^\circ

Step 1: The sum of the interior angles in any triangle is 180∘180^\circ.

∠A+∠ABD+∠ADB=180∘\angle A + \angle ABD + \angle ADB = 180^\circ

Step 2: From the diagram, ∠ADB=90∘\angle ADB = 90^\circ and ∠ABD=60∘\angle ABD = 60^\circ.

Substitute the known values:

∠A+60∘+90∘=180∘\angle A + 60^\circ + 90^\circ = 180^\circ

Step 3: Simplify the equation.

∠A+150∘=180∘\angle A + 150^\circ = 180^\circ ∠A=180∘−150∘\angle A = 180^\circ - 150^\circ ∠A=30∘\angle A = 30^\circ

30^\circ

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