Question

If QS bisects ZRQP, mZRQS =
2x + 10, and mZSQP = 3x - 18,
find mZRQS.

Answer 1

66°

Explanation:

`\because \overrightarrow{QS} \: bisects\: \angle RQP\\\\</p><p>\therefore m\angle RQS = m\angle SQP\\\\</p><p>\therefore 2x + 10 = 3x - 18\\\\</p><p>\therefore 18 + 10 = 3x - 2x\\\\</p><p>\therefore 28 = x\\\\</p><p>\therefore x = 28\\\\</p><p>m\angle RQS = (2x + 10)\degree \\\\</p><p>m\angle RQS = (2* 28+ 10)\degree \\\\</p><p>m\angle RQS = (56+ 10)\degree \\\\</p><p>\huge \purple {\boxed {m\angle RQS =66\degree}} \\\\</p><p>`