Explanation:
We are asked to find the measure of each
exterior angle marked with an “X” in the triangles. Remember this key rule:
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An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.
Alternatively, you can also use:
>
Exterior angle + adjacent interior angle = 180°, since they form a straight line.
We’ll go problem by problem and apply the first rule (sum of remote interior angles), because it’s faster and less error-prone.
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1) Triangle PQR:
Interior angles at P = 49°, at Q = 80°.
Angle ∠QRX is exterior at R, so it's opposite (not adjacent to) angles at P and Q.
So:
m∠QRX = 49° + 80° =
129°
✔ Check: Interior angle at R = 180° − 49° − 80° = 51°, and 51° + 129° = 180° ✔️
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2) Triangle TVU:
Angles at T = 53°, at V = 103°.
Exterior angle ∠VUX is at U, so remote interior angles are at T and V.
m∠VUX = 53° + 103° =
156°
✔ Check: Angle at U = 180 − 53 − 103 = 24°, and 24 + 156 = 180 ✔️
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3) Triangle HFG:
Angles at H = 39°, at G = 26°.
Exterior angle ∠HFX is at F, so remote angles are H and G.
m∠HFX = 39° + 26° =
65°
✔ Check: Angle at F = 180 − 39 − 26 = 115°, and 115 + 65 = 180 ✔️
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4) Triangle KLJ:
Angles at L = 93°, at J = 44°.
Exterior angle ∠JKX is at K, so remote angles are at L and J.
m∠JKX = 93° + 44° =
137°
✔ Check: Angle at K = 180 − 93 − 44 = 43°, and 43 + 137 = 180 ✔️
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5) Triangle ABC:
Angles at A = 21°, at B = 30°.
Exterior angle ∠ACX is at C, so remote angles are A and B.
m∠ACX = 21° + 30° =
51°
✔ Check: Angle at C = 180 − 21 − 30 = 129°, and 129 + 51 = 180 ✔️
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6) Triangle WVU:
Angles at W = 35°, at U = 71°.
Exterior angle ∠WVX is at V, so remote angles are W and U.
m∠WVX = 35° + 71° =
106°
✔ Check: Angle at V = 180 − 35 − 71 = 74°, and 74 + 106 = 180 ✔️
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7) Triangle EFD:
Angles at E = 85°, at D = 63°.
Exterior angle ∠DFX is at F, so remote angles are E and D.
m∠DFX = 85° + 63° =
148°
✔ Check: Angle at F = 180 − 85 − 63 = 32°, and 32 + 148 = 180 ✔️
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8) Triangle MNL:
Angles at N = 75°, at L = 75°.
Exterior angle ∠LMX is at M, so remote angles are N and L.
m∠LMX = 75° + 75° =
150°
✔ Check: Angle at M = 180 − 75 − 75 = 30°, and 30 + 150 = 180 ✔️
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9) Triangle RST:
Angles at R = 47°, at S = 66°.
Exterior angle ∠STX is at T, so remote angles are R and S.
m∠STX = 47° + 66° =
113°
✔ Check: Angle at T = 180 − 47 − 66 = 67°, and 67 + 113 = 180 ✔️
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All answers verified.
Final Answer:
1) 129°
2) 156°
3) 65°
4) 137°
5) 51°
6) 106°
7) 148°
8) 150°
9) 113°
Parent Tip: Review the logic above to help your child master the concept of interior exterior angles worksheet.
