Question

In ∆PQR, PQ = PR and angle P = 40° , then angle Q = ?

Answer 1

Answer:

we know that the sum of a triangle is 180°

let the p and r be x

p + q + r = 180°

40 + x + x = 180°

40+2x = 180°

2x = 180 - 40

2x = 140

x = 140/2

x = 70

q = 70 and r= 70

Answer 2

The measure of  ∠Q is 70°.

Step-by-step explanation:

In the ∆PQR, PQ = PR, which means that the triangle is an isosceles triangle.

An isosceles triangle is one that has two sides equal.

Another property of the isosceles triangle is that the angles opposite to equal sides are also equal.

Thus, if PQ = PR, then ∠R = ∠Q.

Also, according to angle sum property of a triangle,

∠P + ∠Q + ∠R = 180°

Substituting the value of ∠P = 40°, we get

40 + ∠Q + ∠R = 180°

∠Q + ∠R = 180° - 40° = 140°

2∠R = 140° ( since ∠R = ∠Q)

∠R = 70° = ∠Q.

Hence the measure of angle Q is 70°.