Question

What is the measure of angle 2?

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

Answer 1

Correct anwer is option C (37degrees)

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`

Answer 2

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°