Question

Help me solve this problem

Answer 1

x= 50°

Explanation:

I recreated this diagram and attached it.

You can see because of the curved lines that BC and CQ are equal which means that it is an isosceles triangle. In a triangle two sides are equal and the angles of those sides are also equal. which means that ∠ABC=∠CQB.

Let's name them both y, In a triangle, all the angles add up to 180. The other non-equal angle is=100 so we can construct an equation using these data:

2y+100=180

2y= 180-100

y= 80/2= 40°

Look at the line PB and BD. You can see that line PB is a straight verticle line above the horizontal straight line BD. That means that PB is perpendicular to BD and the line PB is perpendicular to BD at the point B so the angle at that point is equal to 90 degrees.

That means that x+y= 90° hence:

x+40°=90°

x= 50°

Answer 2

x = 40°

Explanation:

Given:

BC = CQ

PB ║CQ

∡BCQ = 100°

To Find:

∡PBQ = x = ?

Solution:

In Δ BCQ

∡BCQ + ∡CBQ + ∡BQC = 180°

Sum of interior angle of a triangle is 180°

100 + ∡CBQ + ∡BQC = 180°

Here,

∡CBQ = ∡BQC

Base angle of isosceles triangle

Therefore,

100 + ∡BQC + ∡BQC= 180

2 ∡BQC = 180-100

2 ∡BQC = 80

∡BQC =
`(80)/(2)`

∡BQC = 40°

Again,

∡BQC = ∡PBQ
Being alternate interior angle

Therefore,

x = 40°