Question

The trisectors of angles B and C of scalene triangle ABC meet at points P and Q, as shown. Angle A measures 39 degrees and angle QBP measures 14 degrees. What is the measure of angle BPC?

Answer 1

Answer:

So, the measure of the interior angle of a regular hexagon is 120 degrees. To find the measure of the central angle of a regular hexagon, make a circle in the middle... A circle is 360 degrees around... Divide that by six angles.

Hope it helps!

Answer 2

Given:

A scalene triangle ABC

∠ABQ=∠QBP=∠PBC=14°

∠ACQ=∠QCP=∠PCB

∠BAC = 39°

To find:

Angle BPC

Solution:

The sum of all angles of a triangle =180°

⇒ ∠A + ∠ABC + ∠ACB = 180°

Also, ∠ABC = 3 X ∠QBP = 3 X 14 = 42°

So, ∠ACB = 180 - 39 - 42

= 99°

Since, 3 X ∠ PCB = ∠ACB

⇒ ∠ PCB = 99/3 = 33°

Again applying angle sum property in ΔBPC,

∠PBC + ∠BPC + ∠PCB = 180°

or ∠BPC = 180 - 33 - 14

= 133°

Hence, angle BPC measures 133°.