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

The measure of angle DPA is 39°

Step-by-step 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°

the answer is true.

step-by-step explanation:

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1