Question

MP bisects ∠BMS. If m∠BMP = 2x + 9 and m∠BMS = 7x – 3, find the value of m∠PMS

Answer 1

Explanation:

If MP bisects ∠BMS, then the line MP divides <BMS equally;

The adition postulate if therefore true;

<BMP +< PMS = <BMS and <BMP = < PMS

The equation becomes;

<BMP +< BMP= <BMS

2 <BMP = <BMS

2(2x+9) = 7x - 3

4x+18 = 7x-3

collect like terms

4x-7x = -3-18

-3x = -21

x = 21/3

x = 7

Since <BMP = < PMS 2x+9

< PMS = 2(7)+9

< PMS = 14+9

< PMS = 23

Hence the value of < PMS is 23