Question
In a ∆ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠ BAC = 75°, what is the measure of ∠ PQR (in degrees)?
∠BAC = 75º ∠ABC + ∠ACB + ∠BAC = 180° ∠ABC + ∠ACB + 75° = 180° ∠ABC + ∠ACB = 180° - 75° = 105° Let, ∠ABC = ∠PBQ = 70° and ∠ACB = ∠RCQ = 35° So, ∠PQR = 180° - (∠PQB + ∠RQC) = 180° - [(180° - 2∠PBQ) + (180° - 2∠RQC) [∵ BQ = PQ; QC = QR] = 180° - [(180° - 2 × 70°) + (180° - 2 × 35°)] = 180° - (40° + 110°) = 180° - 150° = 30°More Triangle Questions
- What is the inradius of an equilateral triangle whose vertical height measures 12√3 cm?
- If the side of an equilateral triangle is 12cm, then find the area (in cm 2 ) of the triangle (correct to two decimal places).
- If two triangles PQR and STU are congruent, then which of the following statement(s) is/are true? I. PQ = ST II. ∠PQR = ∠STU
- The vertices of a triangle are given as (5, 4), (9, 6), and (1, 5). Determine the area enclosed by this triangle.
- Given a right-angled triangle with the perpendicular measuring 36 cm and the base measuring 48 cm, determine the length of the shortest median of the trian...
- The base of a right pyramid is an equilateral triangle with side 9 cm. If the height of the pyramid is 45√3 cm, find the volume of the pyramid.
- Area of a triangles with vertices at (2, 3), (-1, 0) and (2, -4) is :
- If the angles of a triangle are in the ratio of 2:5:8, then find the value of the biggest angle.
- In triangle ABC, DE is drawn parallel to BC, intersecting AB at D and AC at E. If AD : DB = 2 : 1 and area of triangle ADE is 24 cm², find: (i) area of tr...
- In a triangle ABC, the incenter is at O. Find angle BAC if angle BOC=120°.
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
