ZWXY is a right angle. If Z is in the interior of ZWXY,
mZWXZ = 7x+8, and
mZZXY = 5x – 2, find the
value of x.

  x = 7

Step-by-step explanation:

The sum of the interior angles is 90°, so you have ...

  (7x +8) +(5x -2) = 90

  12x = 84 . . . . subtract 6; next, divide by 12

  x = 7

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°

50-60=10

step-by-step explanation: