Question

Line AB and CD intersect at P. If angle APC = 2x+30° and angle BPD = 4x -20° then find x angle APC and angle BPD​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of x is 25 and ∠APC = ∠BPD = 80°

GIVEN

Line AB and CD intersect at P. If ∠APC = 2x+30° and ∠BPD = 4x -20°

TO FIND

• Value of x
• ∠APC
• ∠BPD

SOLUTION

We can simply solve the above problem as follows;

We are given,

A̅B̅ and C̅D̅ intersect at P

Therefore,

∠APC = ∠BPD (Vertically opposite angles of lines intersecting at a point are equal)

Therefore,

2x + 30 = 4x-20

Solving for x

30+20 = 4x-2x

50 = 2x

x = 50/2 = 25

Therefore,

The value of x = 25

∠APC = 2x + 30 = 2×25 + 30 = 80°

∠BPD = 4x -20 = 4×25 -20 = 80°

Hence, The value of x is 25 and ∠APC = ∠BPD = 80°

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