Congruent Triangles std8 Page-18.5 EM

Kite ABCD | Find All Angles | Given ∠CAD = 30°, ∠ACB = 50°

📐 Given: ∠CAD = 30° 📐 Given: ∠ACB = 50° 🔷 In Quadrilateral ABCD: AB = AD, CB = CD 📐 Diagonal AC divides Quadrilateral into two triangles

✍️ Find All Angles of Quadrilateral ABCD

1 In ΔADC

In triangle ADC, ∠CAD = 30°, ∠ACD = ? (We need to find this first). What type of triangle is ADC? (Given AB = AD and CB = CD)

2 ∠ACD in ΔADC

Since AD = AB and CD = CB, and AC is common, what can we say about ∠ACD?

3 Value of ∠ACD

From the given data, ∠ACB = 50°. Since the Quadrilateral is symmetric along diagonal AC, what is ∠ACD?

4 ∠ADC (angle at D)

In ΔADC, ∠CAD = 30°, ∠ACD = 50°. Find ∠ADC.

5 In ΔABC

In triangle ABC, ∠ACB = 50°, ∠CAB = ? (Need to find)

6 ∠CAB in ΔABC

By symmetry of the Quadrilateral (AB = AD, CB = CD), ∠CAB equals which angle?

7 Value of ∠CAB

Therefore, ∠CAB = ∠CAD = 30°. Then find ∠ABC in ΔABC.

8 ∠ABC (angle at B)

In ΔABC, ∠CAB = 30°, ∠ACB = 50°. Find ∠ABC.

9 ∠BCD (angle at C)

∠BCD = ∠BCA + ∠ACD = 50° + 50° = ?

10 ∠BAD (angle at A)

∠BAD = ∠BAC + ∠CAD = 30° + 30° = ?

📐 Kite ABCD | Find All Angles