Question
MN is a diameter of a circle with centre O. The tangent
at 'P' meets MN produced at 'Q'. If ∠PMN = 44 ° , then find ∠PNQ.Solution
Angle made by the diameter of a circle on the arc of the circle is 90 o  i.e. ∠MPN = 90 ° .
Sum of each angle in a triangle is 180 o .
So, ∠PMN + ∠PNM + ∠MPN = 180 °
Or, 44 °  + ∠PNM + 90 °  = 180 °
Or, ∠PNM = 180 °  - 134 °
Or, ∠PNM = 46 °
Now, ∠PNM + ∠PNQ = 180 o  (Linear pair of angles)
So, ∠PNQ = 180 - 46 = 134 °
Amit and Sara started a business with the investments of Rs. 20,000 and Rs. 30,000 respectively. After one year, Amit increases his investment by Rs. 5,...
P and Q entered into partnership with Rs. 8000 and Rs. 12000 respectively. After 4 months P withdrew `1/4` of his stock but after 4 months more he put b...
Two firms, X and Y, began a joint venture by investing in a ratio of 9:16. After six months, Firm Y withdrew its entire investment. At the end of the ye...
M and N started a business by investing Rs.4000 and Rs.5000 respectively. After 7 months, M and N increased their investments by 30% and Rs.2400 respect...
‘A’ and ‘B’ invested Rs. 4800 and Rs. 3600, respectively in a business, together. After 6 months, ‘A’ withdrew 25% of his initial investment...
‘A’, ‘B’ and ‘C’ started a business by investing Rs. 3,000, Rs. 3,600 and Rs. 2,400, respectively. After 6 months, ‘B’ decreased his inv...
A, B and C invest in a partnership in the ratio 8:5:10 and investment of A is Rs.200 less than investment of C. Partner B invests for 1/5th and A and C ...
‘A’ invested Rs. 3500 in a business. ‘B’ joined x months later with an investment of Rs. 2500. If at the end of the year, B’s share in the pro...
‘C’ and ‘D’ entered into a business by investing Rs. ‘y’ and Rs. ‘y + 300’, respectively. After 10 months ‘C’ invested Rs. 400 more ...
P and Q started a business by investing Rs.5600 and Rs.4000 respectively. After 6 months, Q increased his investment by a certain percentage such that a...
Relevant for Exams:
