In the diagram, square ABCD has sides of length 4, and triangle ABE is equilateral. Line segments BE and AC intersect at P. Point Q is on BC so that PQ is perpendicular to BC and PQ=x.

Determine the measure of angle BPC.

Lightning Dec 2, 2018

#1**+2 **

Let's look at triangle BPC

Angle C is 45 degrees (bisected by the diagonal)

Angle ABE is 60 degrees due to equilateral triangle so angle B = 30 degrees

180 -30 - 45 = angle BPC = 105 degrees

ElectricPavlov Dec 2, 2018

#1**+2 **

Best Answer

Let's look at triangle BPC

Angle C is 45 degrees (bisected by the diagonal)

Angle ABE is 60 degrees due to equilateral triangle so angle B = 30 degrees

180 -30 - 45 = angle BPC = 105 degrees

ElectricPavlov Dec 2, 2018