Question

In a quadrilateral ABCD,AB=20m DC=13m<BCD=136,<ADC=127,if BC and DP produced meet at P,find angle CP

Answer 1

To find angle CP, we need to consider the properties of quadrilaterals and the given angle measures.

Step 1: Let's start by drawing quadrilateral ABCD with the given measurements.

A____________________B
\ /
\ /
C________________D

Step 2: We know that opposite angles in a quadrilateral are supplementary, meaning they add up to 180 degrees. Therefore, we can find angle ACD by subtracting angle BCD from 180 degrees.

A____________________B
\ /
\ BCD /
\ /
\ /
C_________/DC=13m
\ /
\ /
D

Angle ACD = 180° - angle BCD
= 180° - 136°
= 44°

Step 3: Since opposite angles in a quadrilateral are supplementary, angle ADC is equal to angle ACD. Therefore, angle ADC is also 44°.

A____________________B
\ /
\ BCD /
\ /
\ /
C_________/DC=13m
Angle ADC=44°
\ /
\ /
D

Step 4: Angle DCP can be found by subtracting angle ADC from 180 degrees since angle DCP and angle ADC are adjacent and supplementary.

A____________________B
\ /
\ BCD /
\ /
\ /
C_________/DC=13m
Angle ADC=44°
\ /
\ /
D___CP__P

Angle DCP = 180° - angle ADC
= 180° - 44°
= 136°

Therefore, angle CP is equal to 136 degrees.