To solve this worksheet, we need to use the
Exterior Angle Theorem.
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🔷 Exterior Angle Theorem:
> The measure of an exterior angle of a triangle is equal to the
sum of the measures of the two remote interior angles (the two angles inside the triangle that are not adjacent to the exterior angle).
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Let’s go problem by problem:
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✔ Problem 1:
Triangle PQR with ∠P = 49°, ∠Q = 80°.
Exterior angle at R:
∠QRX
Remote interior angles: ∠P and ∠Q
→ m∠QRX = 49° + 80° =
129°
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✔ Problem 2:
Triangle TVU with ∠T = 53°, ∠V = 103°.
Exterior angle at U:
∠VUX
Remote interior angles: ∠T and ∠V
→ m∠VUX = 53° + 103° =
156°
*(Note: Even though ∠V is obtuse, it’s still one of the remote interior angles for the exterior angle at U.)*
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✔ Problem 3:
Triangle HFG with ∠H = 39°, ∠G = 26°.
Exterior angle at F:
∠HFX
Remote interior angles: ∠H and ∠G
→ m∠HFX = 39° + 26° =
65°
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✔ Problem 4:
Triangle JKL with ∠J = 44°, ∠L = 93°.
Exterior angle at K:
∠JKX
Remote interior angles: ∠J and ∠L
→ m∠JKX = 44° + 93° =
137°
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✔ Problem 5:
Triangle ABC with ∠A = 21°, ∠B = 30°.
Exterior angle at C:
∠ACX
Remote interior angles: ∠A and ∠B
→ m∠ACX = 21° + 30° =
51°
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✔ Problem 6:
Triangle WUV with ∠W = 35°, ∠U = 71°.
Exterior angle at V:
∠WVX
Remote interior angles: ∠W and ∠U
→ m∠WVX = 35° + 71° =
106°
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✔ Problem 7:
Triangle DEF with ∠E = 85°, ∠D = 63°.
Exterior angle at F:
∠DFX
Remote interior angles: ∠D and ∠E
→ m∠DFX = 63° + 85° =
148°
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✔ Problem 8:
Triangle MNL with ∠N = 75°, ∠L = 75°.
Exterior angle at M:
∠LMX
Remote interior angles: ∠N and ∠L
→ m∠LMX = 75° + 75° =
150°
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✔ Problem 9:
Triangle RST with ∠R = 47°, ∠S = 66°.
Exterior angle at T:
∠STX
Remote interior angles: ∠R and ∠S
→ m∠STX = 47° + 66° =
113°
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✔ Final Answers:
1)
m∠QRX = 129°
2)
m∠VUX = 156°
3)
m∠HFX = 65°
4)
m∠JKX = 137°
5)
m∠ACX = 51°
6)
m∠WVX = 106°
7)
m∠DFX = 148°
8)
m∠LMX = 150°
9)
m∠STX = 113°
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✔ All answers are found using the
Exterior Angle Theorem:
Exterior Angle = Sum of Two Remote Interior Angles
This is a powerful shortcut — you don’t need to find the third interior angle or use 180° unless asked! Just add the two non-adjacent angles.
Parent Tip: Review the logic above to help your child master the concept of exterior angles of triangles worksheet.
