A state government has made three new bus stops, situated at P. Q. R as shown in figure, which is operated by the state Transport Co-operation. These three bus stops are equidistant from each other. Consider the above problem and answer the following questions:
(a) Which type of triangle is A PQR?
(c) If QR = 8 cm, then what is the value of RP + PQ?
(b) What is the measure angle PQR?
(d) What is the measure of angle QOR?
(e) What is the value of (L0QR+ LORQ)?
Answers
Answer:
As given below
Step-by-step explanation:
Given data
A state government has made 3 bus stops P, Q, and R
which are operated by state transport co-operation
These bus stops are at equidistant from each other
answers for the given questions
(a) Which type of triangle is ΔPQR?
⇒ from given data the bus stops are at equidistant from each other then the side of the triangle PQR are equal
⇒ ΔPQR is a equilateral triangle
(b) What is the measure angle PQR?
⇒ In a triangle if the sides are equal then the angles are also equal
⇒ let a be the each angle in PQR
⇒ we know that sum of the angles in triangle = 180°
⇒ a + a + a = 180° ⇒ 3a =180° ⇒ a = 60°
⇒ each angle in triangle PQR is 60°
⇒ Angle PQR = 60°
(c) If QR = 8 cm, then what is the value of RP + PQ?
⇒ given QR = 8 cm
⇒ from given data P, Q, R are at equidistant
⇒ RP + PQ = 8 cm + 8 cm = 16 cm
(d) What is the measure of angle QOR?
⇒ from (b) each angle in triangle is 60°
⇒ If "O" is a point where OR and OQ bisects the angles ∠PRQ and ∠PQR respectively then ∠ORQ = 30° and ∠OQR =30°
⇒ ∠QOP = 180° - [ ∠ORQ + ∠OQR ]
= 180° - [30 + 30] = 180° -60° = 120°
⇒ Angle QOR = 120°
(e) What is the value of (∠0QR+ ∠ORQ)?
⇒ from (d) ∠OQR + ∠ORQ = 30° + 30° = 60°