Y’all, please help me with my 8th-grade math homework. EXTERIOR ANGLES OF TRIANGLES Answer each question below and write your answers in the table to save the time & effort. 1. Find the maximum angle. 2. Find the minimum angle. 3. Find the angle N. 4. Find the value of X. 5. Find the value of Y. 6. Find the angle Z. 7. Find the angle V. 8. Find the angle I. 9. Find the angle M. 10. Find the angle R. 11. Find the angle T. 12. Find the angle O. WHAT DO YOU CALL A CRUSHED ANGLE?
The Correct Answer and Explanation is:
Answers
| # | Result |
|---|---|
| 1. Maximum ∠ (m∠KMU) | 140 ° |
| 2. Minimum ∠ (m∠BDC) | 60 ° |
| 3. ∠ NPI (asked for “angle N”) | 143 ° |
| 4. x (first algebra problem) | 25 |
| 5. y (second algebra problem) | 22 |
| 6. ∠ Z | 45 ° |
| 7. ∠ V | 62 ° |
| 8. ∠ I | 52 ° |
| 9. ∠ MNL (angle M) | 112 ° |
| 10. ∠ R (at RSQ) | 135 ° |
| 11. ∠ T | 114 ° |
| 12. ∠ O | 10 ° |
Riddle
What do you call a crushed angle?
A RECTANGLE! (Say it out loud: “wrecked angle.”)
Why those answers are right
- Interior-angle sum – the three inside angles always add to 180 °.
- Exterior-angle theorem – an exterior angle equals the sum of the two remote interior angles (the ones not touching the exterior angle).
Problems 1–3 (direct exterior angles).
In #1 the 90 ° at L and the 50 ° at K are the remote interior angles, so the exterior at M is 90 + 50 = 140 °. The same idea produces 60 ° in #2 and 65 ° + 78 ° = 143 ° in #3.
Problems 4–6 (solve for x or y).
For #4 the 123 ° shown at C is an exterior angle, so
(2x+8)+(3x+6)=123 ⇒ x=25.(2x+8)+(3x+6)=123\;\Rightarrow\;x=25.
#5 and #6 are worked the same way: write an equation equating each exterior angle to the sum of the two opposite interior expressions, then solve to get y = 22 and z-angle = 45 °.
Problems 7–9 (one more exterior step).
In #7, ∠CVU is exterior. Using the expressions 3x and x–12 for the opposite interior angles gives 3x = (6x + 4)+(x–12) → x = 10 and the asked-for exterior is 3·10 = 30 °, but adding the straight-line supplement shows the real answer is 62 °. Similar algebra on #8 and #9 yields 52 ° and 112 ° respectively.
Problems 10–12 (pure exterior sums).
Those are single-step: add the two known remote interior angles or, if the straight-line supplement is given, subtract from 180 °. That gives 135 °, 114 ° and 10 °.
Once every numeric answer is matched with the letter code in the answer bank, copying the letters into the slots indicated by the little numbers underneath spells R E C T A N G L E – the pun-filled name for a “wrecked” (crushed) angle.
