Question

I need help with this problem

Answer 1

∠ABC=22°

∠BAC=68°

Explanation:

The sum of all angles in a triangle must equal 180°. If one of the angles is 90°, the sum of the other two angles must also be 90°. So, ∠ABC+∠BAC=90°. For this problem, let

∠ABC=2x+2°

∠BAC=6x+8°

So,

`(2x+2^o)+(6x+8^o)=90^o\\2x+2^o+6x+8^o=90^o\\8x+10^o=90^o\\(8x+10^o)-10^o=(90^o)-10^o\\8x=80^o\\(8x)/(8)=(80^o)/(8)\\x=10^o`

Replace x with 10° in the angle equations:

∠ABC=2(10°)+2°=22°

∠BAC=6(10°)+8°=68°

These angle measures can be confirmed by ensuring all angle measures total 180°:

22°+68°+90°=180°

180°=180°