BRAINLIST In the above figure, m∠P = 130° and m∠Q = (5x)°. If angles P and Q are supplementary angles, what are the value of x and the measure of angle Q?

A.
x = 62, m∠Q = 50°
B.
x = 44, m∠Q = 220°
C.
x = 10, m∠Q = 50°
D.
x = 10, m∠Q = 15°

C x = 10  Q = 50

Step-by-step explanation:

supplemantary means adds to 180 deg.

so 130 + 5x = 180

5x = 50 = ang. Q

x = 50/5 = 10 deg.

x= 12 and Angle Q measures 60 degrees

Step-by-step explanation:

Supplementary angles are two angles added together to make 180.

So 5x +120= 180  subtract 120 from both sides

5x=60  divide both sides by 5

x= 12

Angle Q= 5 times 12 = 60

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

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step-by-step explanation:

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