Question

In the figure, circle with centre D touches the sides of ∠ACB at A. If ∠ACB = 52°, complete the activity to find the measure of ∠ADB.

Activity:

ln `square` ABCD,

∠CAD = ∠CBD = `square`°     ....Tangent theorem

∴ ∠ACB + ∠CAD + ∠CBD + ∠ADB = `square`°

∴ 52° + 90° + 90° + ∠ADB = 360° 

∴ ∠ADB + `square`° = 360°

∴ ∠ADB = 360° − 232°

∴ ∠ADB = `square`°

Answer 1

ln `square` ABCD,

∠CAD = ∠CBD = \[\boxed{90}\]°     ....Tangent theorem

∴ ∠ACB + ∠CAD + ∠CBD + ∠ADB = \[\boxed{360}\]°

∴ 52° + 90° + 90° + ∠ADB = 360° 

∴ ∠ADB + \[\boxed{232}\] = 360°

∴ ∠ADB = 360° − 232°

∴ ∠ADB = \[\boxed{128}\]°