15 Questions
If AB || CD || EF and CE || DF, then find the value of x, y, and z.
x = 45°, y = 80°, z = 30°
If l || m, then find the value of θ.
70°
If l || m and A || B, then find the value of θ.
95°
If QR || PS & PQ = QR, then find the value of θ.
110°
If l || m and A || B, then find the value of θ.
40°
If l || m II n, then find the value of θ.
128°
Find the value of ∠BOC in triangle ABC if ∠A = 50° and the interior bisector of ∠B and ∠C intersects at point O.
27°
In triangle ABC, if AB = 6 cm, AC = 4 cm, and BC = 7 cm, then find the length of BD where AD is the interior bisector of ∠A.
3.5 cm
Find the value of ∠ACB in triangle ABC if ∠AOB = 125° and the interior bisector of ∠A and ∠B intersects at point O.
27.5°
In triangle ABC, if AB = 10 cm, AC = 14 cm, and BC = 6 cm, then find the length of BD where AD is the interior bisector of ∠A.
7 cm
Find the value of ∠BOC in triangle ABC if ∠A = 30° and the exterior bisector of ∠B and ∠C intersects at point O.
15°
In triangle ABC, if AB = 5 cm, BC = 8 cm, and CA = 4 cm, then find the length of AF, CE, and BD where AD, BE, and CF are the interior bisectors of ∠A, ∠B, and ∠C respectively.
AF = 2.5 cm, CE = 4 cm, BD = 4 cm
Find the value of ∠BOC in triangle ABC if the interior bisector of ∠B and the exterior bisector of ∠C intersects at point O, and ∠A = 84°.
84°
In triangle ABC, if AB = 10 cm, BC = 15 cm, ∠C = 30°, and ∠BDC = 130°, then find the value of ∠ABC where D is a point on the side AC and AD : DC = 2 : 3.
50°
In triangle ABC, if AD is the exterior bisector of ∠A and AB = 6 cm, BC = 5 cm, and AC = 4 cm, then find the length of CD.
2 cm
Study Notes
Conditions for Parallel Lines
- If AB || CD || EF, then CE || DF.
- If l || m, then θ is unknown.
- If l || m and A || B, then θ is unknown.
- If QR || PS and PQ = QR, then θ is unknown.
- If l || m II n, then θ is unknown.
Angle Properties in Triangles
- In triangle ABC, if ∠A = 50° and the interior bisector of ∠B and ∠C intersects at point O, then ∠BOC is unknown.
- In triangle ABC, if ∠AOB = 125° and the interior bisector of ∠A and ∠B intersects at point O, then ∠ACB is unknown.
- In triangle ABC, if ∠A = 30° and the exterior bisector of ∠B and ∠C intersects at point O, then ∠BOC is unknown.
- In triangle ABC, if the interior bisector of ∠B and the exterior bisector of ∠C intersects at point O, and ∠A = 84°, then ∠BOC is unknown.
Length Properties in Triangles
- In triangle ABC, if AB = 6 cm, AC = 4 cm, and BC = 7 cm, then the length of BD is unknown where AD is the interior bisector of ∠A.
- In triangle ABC, if AB = 10 cm, AC = 14 cm, and BC = 6 cm, then the length of BD is unknown where AD is the interior bisector of ∠A.
- In triangle ABC, if AB = 5 cm, BC = 8 cm, and CA = 4 cm, then the lengths of AF, CE, and BD are unknown where AD, BE, and CF are the interior bisectors of ∠A, ∠B, and ∠C respectively.
- In triangle ABC, if AB = 10 cm, BC = 15 cm, ∠C = 30°, and ∠BDC = 130°, then the value of ∠ABC is unknown where D is a point on the side AC and AD : DC = 2 : 3.
- In triangle ABC, if AD is the exterior bisector of ∠A and AB = 6 cm, BC = 5 cm, and AC = 4 cm, then the length of CD is unknown.
Test your knowledge of geometry angles with these multiple-choice questions. Analyze parallel lines and transversals to find the measures of various angles.
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