Answer:
Angle A: 28 degrees
Angle B: 24 degrees
Step-by-step explanation:
Hi there!
The angle that measures 52 degrees (angle DCA) is one of the exterior angles of a triangle. An exterior angle of a triangle is equal to the sum of the opposite interior angles, which in this case would be angles A and B. Knowing this, we can set up the following equation:
[tex]4y-4+3y=52[/tex]
1) Solve for y
[tex]4y-4+3y=52[/tex]
Combine like terms
[tex]7y-4=52[/tex]
Add 4 to both sides to isolate 7y
[tex]7y-4+4=52+4\\7y=56[/tex]
Divide both sides by 7
[tex]\frac{7y}{7}=\frac{56}{7} \\y=8[/tex]
Therefore, y is equal to 8.
2) Solve for angles A and B
Angle A:
[tex]4y-4\\=4(8)-4\\=32-4\\=28[/tex]
Angle B:
[tex]3y\\=3(8)\\=24[/tex]
I hope this helps!
