Question

Given: measurement of arc AB=(5x+10)° , measurement of arc BC=(x+1)°,

measurement of arc CD=3x°, measurement of arc DA=(3x+25)°.
Find: m∠DPA

Answer 1

39 degrees

Explanation:

Answer 2

The measure of angle DPA is 39°

Explanation:

step 1

Find the value of x

we know that

arc AB+arc BC+arc CD+arc DA=360°

substitute the values

(5x+10)°+(x+1)°+3x°+(3x+25)°=360°

Solve for x

(12x+36)°=360°

12x=360°-36°

x=324°/12=27°

step 2

Find the measure of angle DPA

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

m∠DPA=(1/2)[arc DA-arc BC]

arc DA=3(27)+25=106°

arc BC=27+1=28°

substitute the values

m∠DPA=(1/2)[106°-28°]=39°