Final Answer:
1. $ x = 50^\circ $
2. $ x = 60^\circ $
3. $ x = 40^\circ $
4. Yes — because the angles add to $ 180^\circ $: $ 42 + 58 + 70 = 170^\circ $? Wait — that’s
not 180°. So actually:
No, a triangle cannot have angles $ 42^\circ, 58^\circ, 70^\circ $, since they sum to $ 170^\circ $, not $ 180^\circ $.
5. $ x = 60^\circ $
6. $ x = 70^\circ $
7. $ x = 50^\circ $, $ y = 130^\circ $
8. $ x = 40^\circ $
Wait — let me double-check each carefully using triangle angle rules:
1. Triangle with angles $ 60^\circ $, $ 70^\circ $, and $ x $.
$ x = 180 - 60 - 70 = 50^\circ $
2. Equilateral-looking triangle (all sides marked equal) → all angles equal → $ x = 60^\circ $
3. Right triangle: one angle $ 90^\circ $, another $ 50^\circ $, so $ x = 180 - 90 - 50 = 40^\circ $
4. Angles: $ 42^\circ, 58^\circ, 70^\circ $. Sum = $ 42 + 58 = 100 $, $ 100 + 70 = 170 \ne 180 $. So
No, not possible.
5. Right triangle: $ 90^\circ $, $ 30^\circ $, so $ x = 180 - 90 - 30 = 60^\circ $
6. Triangle with two equal sides (isosceles), base angles equal. One base angle is $ 55^\circ $, so other base angle also $ 55^\circ $, then $ x = 180 - 55 - 55 = 70^\circ $
7. Exterior angle $ 130^\circ $, adjacent interior angle $ y $: $ y = 180 - 130 = 50^\circ $. Then triangle has angles $ 30^\circ $, $ y = 50^\circ $, and $ x $. So $ x = 180 - 30 - 50 = 100^\circ $? Wait — but the diagram likely shows $ x $ as the *other* interior angle, and the $ 130^\circ $ is exterior to angle $ y $, with $ x $ and $ 30^\circ $ inside. Let me re-evaluate based on standard layout:
In problem #7, typical setup: triangle with one interior angle $ 30^\circ $, another interior angle labeled $ x $, and an exterior angle $ 130^\circ $ adjacent to the third interior angle (call it $ y $). Then:
- $ y + 130 = 180 \Rightarrow y = 50^\circ $
- Sum: $ x + 30 + 50 = 180 \Rightarrow x = 100^\circ $
But the user’s answer space says “x and y”, so both needed. So:
$ y = 50^\circ $, $ x = 100^\circ $
8. Triangle with angles $ 60^\circ $, $ 80^\circ $, and $ x $. So $ x = 180 - 60 - 80 = 40^\circ $
So correcting earlier mistake in #7:
Final Answer:
1. $ 50^\circ $
2. $ 60^\circ $
3. $ 40^\circ $
4. No
5. $ 60^\circ $
6. $ 70^\circ $
7. $ x = 100^\circ $, $ y = 50^\circ $
8. $ 40^\circ $
Parent Tip: Review the logic above to help your child master the concept of printable math worksheets exterior angles.
