Answer:
The answer is going to be C.
Step-by-step explanation:
To help you in the future with any question like this one, you can always use Desmos Calculator.
Remark
There's a lot you don't know here. Are DE and GF parallel? Is B a right angle? You can't assume that it is. The safest way to proceed is to give x in terms of 58 and B. You might get an answer that gives you something like 32 but I don't think you can say that unless you are told somewhere that ABC is a right angle triangle with the right angle at B.
So what to do.
<BAC = 58o That's because <BAC = <IAK They vertically opposite.
<ABC + <BAC + <ACB = 180o All triangles have 180o
<ACB = 180 - 58 - <ABC Solve for an unknown angle of a triangle.
<ACB = 122 - <ABC
x = <ACB Vertically opposite angles.
x = 122 - <ABC Answer It's 32 if ABC is a right angle.
Answer:
C. x = 3, y = 2
Step-by-step explanation:
If both triangles are congruent by the HL Theorem, then their hypotenuse and a corresponding leg would be equal to each other.
Thus:
x + 3 = 3y (eqn. 1) => equal hypotenuse
Also,
x = y + 1 (eqn. 2) => equal legs
✔️Substitute x = y + 1 into eqn. 1 to find y.
x + 3 = 3y (eqn. 1)
(y + 1) + 3 = 3y
y + 1 + 3 = 3y
y + 4 = 3y
y + 4 - y = 3y - y
4 = 2y
Divide both sides by 2
4/2 = 2y/2
2 = y
y = 2
✔️ Substitute y = 2 into eqn. 2 to find x.
x = y + 1 (eqn. 2)
x = 2 + 1
x = 3
