Question

Use all of the angle relationships that we have covered to find the missing angles in the puzzle below

Answer 1

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

I started with triangle GHJ on the right. It is isosceles, so ...

  g = 48°

  h = 2(90 -g) = 84°

  k = 180° -h = 96°

Then, on the lower right, we have ...

  a = 180° -143° = 37°

  b = 143°

  c = e = a = 37°

  f = 90° -e = 53°

At vertex D, we also have ...

  85° +d = b  ⇒  d = 143° -85° = 58°

In triangle DGH, we have ...

  m + d = h  ⇒  m = h -d = 84° -58° = 26°

The sum of angles in triangle DGP is 180°, so ...

  p = 180° -85° -26° = 69°

Finally, ...

  s = p = 69°

  r = 180° -p = 111°

_____

The relationships we used are ...

• corresponding angles are congruent (at a transversal of parallel lines)
• alternate interior angles are congruent
• an exterior angle equals the sum of remote interior angles
• acute angles in a right triangle are complementary
• angles in a triangle sum to 180°
• linear pair angles are supplementary
• angle sum theorem

Answer 2

Answer:

Answer: $4,664

Step-by-step explanation:

Direct Variation can be set up as a proportion:

\dfrac{\text{Property Tax}}{\text{Assessed Valuation}}:\dfrac{1590}{81,000}=\dfrac{x}{237,600}

Assessed Valuation

Property Tax

:

81,000

1590

=

237,600

x

Cross Multiply: x = 4664