Question

What is the measure of angle 2?

A) 47 degrees
B) 74 degrees
C) 37 degrees
D) 53 degrees

Answer 1

y = x + 3
3 x + 2 = y + 1
3 x + 2 = x + 3 + 1 
2 x = 2
x = 1,   y = x + 3 = 4
We have:  3 x + 2 = y + 1 and: y = x + 3.
It means that we have 4 equal triangles ( O is the centre ):
ΔTOS,  ΔSOR,  ΔROQ,  ΔQOT.
∠ 1 = 53°
∠ 2 = (180° - 2 · 53°) : 2 = 37°
Answer: C ) 37° 
 

Answer 2

Answer:

Correct anwer is option C (37degrees)

Step-by-step explanation:

We know that the diagonals of a rhombus bisect each other and perpendicular to each other and and diagonals bisect the angles

therefore from given figure it is clear that

In $\triangle TOS$ by angle sum property

$\angle TOS=90 \\\angle1=53$

$\angle1+\angle2+90=180\\53+\angle2=180-90\\\angle2=90-53\\\angle2=37degrees$