Question

Please help with 3. 4. 5.

Answer 1

3.

`\text{The Triangle Sum Theorem:}\\m\angle A+m\angle B+m\angle C=180^o`

`x+2x-1+3x+1=180\\6x=180\ \ \ |:6\\x=30`

`x^o=30^o\\(3x+1)^o=(3\cdot30+1)^o=91^o\\(2x-1)^o=(2\cdot30-1)^o=59^o`
4.

`r-6+3r-3+5r=180\\9r-9=180\ \ \ |+9\\9r=189\ \ \ |:9\\r=21`

`(r-6)^o=(21-6)^o=15^o\\(3r-3)^o=(3\cdot21-3)^o=60^o\\(5r)^o=(5\cdot21)^o=105^o`
5.

`\text{The Exterior Angle Theorem:}\\m\angle CAB+m\angle ABC=m\angle DCB`

`2g+9g=110\\11g=110\ \ \ |:11\\g=10`

`m\angle A=2\cdot10^o=20^o\\m\angle ACB=180^o-110^o=70^o\\m\angle B=9\cdot10^o=90^o`