Question

. In Fig. 12.21, the
bisectors of angleP
and angleQ meet at
a point O. If angleR
= 100° and angleS
= 50°, find anglePOQ​

Answer 1

Answer:

75°

Step-by-step explanation:

angle S+angle R+angle P+angle Q=360°

angle P+angleQ=360°-150°

angle P+angleQ=210°

let angle OPQ be x and PQO be y

angle P = angle OPQ/2=x/2

angleQ=anglePQO/2=y/2

x/2+y/2=210°/2

x/2+y/2=105°

angleOPQ+anglePQO+anglePOQ=180°

105°+anglePOQ=180°

anglePOQ=180°-105°

anglePOQ=75°