Question

Lines AC and BD intersect at point P. m∠APD = 47° Find the measures of ∠APB, ∠BPC, ∠CPD.

Answer 1

∠APD and ∠APB are angles in a linear pair. 

∴m∠APD + m∠APB = 180° 

∴47 + m∠APB = 180

∴47 + m∠APB – 47 = 180 – 47 …. (Subtracting 47 from both sides) 

∴m∠APB = 133° 

m∠CPD = m∠APB = 133° … .(Vertically opposite angles) 

m∠BPC = m∠APD = 47° … .(Vertically opposite angles) 

∴The measures of ∠APB, ∠BPC and ∠CPD are 133° , 47° and 133° respectively.