Question

Angle APC and angle BPD are vertically opposite angle. If angle APD=3x-20 and angle BPD=2x+30, then find angle x and also find angle APD and angle BPD​

Answer 1

Answer:

x=50

Step-by-step explanation:

APC = 3x - 20

BPD = 2x + 30

APC = BPD

3x - 20 = 2x + 30

3x - 2x = 30 + 20

x = 50

Answer 2

x = 50

The angle measure 130 degrees.

Step-by-step explanation:

We are given the following in the question:

$\angle APC = 3x -20\\\angle APD = 2x + 30$

$\angle APC, \angle BPD \text{ are vertically opposite angles}$

Thus, by property of vertically opposite angle,

$\angle APC =\angle APD$

Equating the two angles, we get,

$3x - 20 = 2x + 30\\3x - 2x = 30 + 20\\x = 50$

Thus, the value of x is 50.

Measure of angle:

$\angle APC = 3(50)-20 = 130^\circ\\\angle APD = 2(50) + 30 = 130^\circ$

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