Question

In the adjacent figure, seg AB || seg AD, seg BC || seg BD, angle BAD = 70 , angle BCD = 65. find the values of x, y , z and p.

Answer 1

Answer:

135°

Step-by-step explanation:

<BAD + <BCD = 70° + 65° = 135°

Answer 2

• x is equal to 55°, y is equal to 55°, z is equal to 65° and p is equal to 50° .

Given :-

• seg AB = seg AD
• seg BC = seg BD
• ∠BAD = 70°
• ∠BCD = 65°

To Find :-

• Values of x, y, z and p ?

Concept used :-

• Angle opposite to equal sides of a triangle are equal in measure .
• Sum of all three angles of triangle is equal to 180° .

Solution :-

In ∆ABD we have,

→ seg AB = seg AD

So,

→ ∠ADB = ∠ABD { Angle opposite to equal sides of a triangle are equal in measure }

→ x = y ------- Equation (1)

also,

→ ∠BAD = 70° { given }

then,

→ ∠BAD + ∠ABD + ∠ADB = 180° { Angle sum property of a ∆ }

→ 70° + x + y = 180°

→ x + x = 180° - 70° { using Equation (1) }

→ 2x = 110°

dividing both sides by 2,

→ x = 55°

therefore,

→ x = y = 55°

Similarly, In ∆BCD we have,

→ seg BC = seg BD

So,

→ ∠BDC = ∠BCD { Angle opposite to equal sides of a triangle are equal in measure }

also,

→ ∠BCD = 65° { given }

then,

→ ∠BDC = 65°

→ z = 65°

now,

→ ∠BCD + ∠BDC + ∠CBD = 180° { Angle sum property of a ∆ }

→ 65° + 65° + p = 180°

→ 130° + p = 180°

→ p = 180° - 130°

→ p = 50°

Hence, the values of x, y, z and p are 55°, 55° , 65° and 50° respectively .

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