Answer:
Explanation:
Remark
This may be a little late, but it is well worth finding all the answers. It is a perfect test question.
You should solve the angles in this order 2 5 1 4 3. This is not the only order you could use.
Angle 2
<180 = <2 + 148 <2 and 148 are supplementary
<180- 148 = <2
<2 = 32
Angle 5
1) All triangles have 180 degrees.
2) Diagonal bisect each other and are equal.
3) The two sides (one of which is opposite angle 5 are equal.
x + x + 148 = 180 All triangles have 180 degrees
All rectangles have diagonals that are bisected and the bisected parts are equal.
2x + 148 = 180 Subtract 148
2x = 180 - 148
2x = 32 Divide by 2
x = 32/2
x = 16
But x is really <5
<5 = 16
Angle 1
<1 = <5 by the z property of angles associated with parallel lines.
Angle 4
Angle 4 and <5 are Complementary. They make up 90 degrees.
Angle 3
<2 + the two base angles in the triangle = 180 degrees
The two base angles are equal. Call them x.
x + x + 32 = 180
2x + 32 = 180 Subtract 32 from both sides
2x = 180-32
2x = 148 Divide by 2
x = 148/2
x = 74
<3 = 72