Answer:
![m\angle{W} = {75{^\circ}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/3yjzuwx69ggnrypqdwqpnjnjlvr53p3ist.png)
![m\angle{Y} = {15{^\circ}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/5nkk9ovb619vrdzfqt8sl9za26czl8neib.png)
![m\angle{Z} = {90{^\circ}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/u5r5bnm12huab7ym96mqm093hcpehkfonz.png)
Explanation:
All angles in a triangle must add up to
![180{^\circ}](https://img.qammunity.org/2023/formulas/mathematics/high-school/243rvs0uq7edn5rrm725lze9a7503flfsy.png)
First we can use an equation to find
![x](https://img.qammunity.org/2023/formulas/mathematics/high-school/7i9rhkmy8weow049o4r221u9e7b2s5rdwo.png)
![(x - 15) + (2x - 165) + 90 = 180](https://img.qammunity.org/2023/formulas/mathematics/high-school/ifdt0z666m06ohpzakiaat3jzfma42xpgu.png)
![3x - 180 = 90](https://img.qammunity.org/2023/formulas/mathematics/high-school/n9nd1fc97a8akljow4mu5ejrtdqg8ta372.png)
![3x = 270](https://img.qammunity.org/2023/formulas/mathematics/high-school/bq1lqteck2bevsep7veecmld13z2kj0wat.png)
![x = 90](https://img.qammunity.org/2023/formulas/mathematics/high-school/a8i1ujce2oz909zxrxhgeoaqv8n4kw6l1v.png)
Now we can solve for
and
through substitution
![\angle{W} = 90 - 15 \rightarrow \boxed{75{^\circ}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/4gph88ks2mo4yco29xox8i63wpix7hvj5x.png)
![\angle{Y} = 2x - 165 \rightarrow 2(90) - 165 \rightarrow 180 - 165 \rightarrow \boxed{15{^\circ}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ir7vq172qnee20b05edzzncvsuxq81kbfh.png)
Now we can classify the triangle
It is right because it has a
angle
These are the answers
- Kan Academy Advanced