Question

can someone please help and explain to me on how to do this geometry question please?! Thank youuuuu!!! ❤

Answer 1

There are 13 angles.
We know that $m\angle4=112$ and $m\angle12=105$ (11 angles)

1.

$m\angle2+m\angle3+m\angle4=180\qquad\qquad\text{linear angles}\\\\m\angle3+m\angle3+m\angle4=180\qquad\qquad m\angle2=m\angle3\\\\2m\angle3+m\angle4=180\\\\2m\angle3+112=180\\\\2m\angle3=180-112\\\\2m\angle3=68\quad|:2\\\\\boxed{m\angle3=34=m\angle2}$

(9 angles)

2.

$m\angle3+m\angle12+m\angle11=180\qquad\qquad\text{triangle}\\\\34+105+m\angle11=180\\\\139+m\angle11=180\\\\m\angle11=180-139\\\\\boxed{m\angle11=41}$

(8 angles)

3.

$m\angle12+m\angle13=180\qquad\qquad\text{linear angles}\\\\105+m\angle13=180\\\\m\angle13=180-105\\\\\boxed{m\angle 13=75}$

(7 angles)

4.

$m\angle1+m\angle2+m\angle13=180\qquad\qquad\text{triangle}\\\\m\angle1+34+75=180\\\\m\angle1+109=180\\\\m\angle1=180-109\\\\\boxed{m\angle1=71}$

(6 angles)

5.

$m\angle9=m\angle11\qquad\qquad\text{vertical angles}\\\\\boxed{m\angle9=41}$

(5 angles)

6.

$m\angle10+m\angle11=180\qquad\qquad\text{linear angles}\\\\m\angle10+41=180\\\\m\angle10=180-41\\\\\boxed{m\angle10=139}$

(4 angles)

7. $a||b\text{ and } c||d$ so we have a parallelogram.

$m\angle4+m\angle5=180\qquad\text{consecutive angles are supplementary}\\\\112+m\angle5=180\\\\m\angle5=180-112\\\\\boxed{m\angle5=68}$

(3 angles)

$m\angle8=m\angle5\qquad\qquad\text{opposite angels are congruent}\\\\\boxed{m\angle8=68}$

(2 angles)

8.

$m\angle7+m\angle8+m\angle9=180\qquad\qquad\text{triangle}\\\\m\angle7+68+41=180\\\\m\angle7+109=180\\\\m\angle7=180-109\\\\\boxed{m\angle7=71}$

(1 angle)

9.

$m\angle1+m\angle5+m\angle6=180\qquad\qquad\text{triangle}\\\\71+68+m\angle6=180\\\\139+m\angle6=180\\\\m\angle6=180-139\\\\\boxed{m\angle6=41}$