Help me to do exercise no 4​

y=50 and z=60 (vertically opposite)

x+60+y=180

or x+60+50=180

or x+110=180

or x=70

Step-by-step explanation:

a.x = 95 degree

reason = being vertically opposite angles

x + 145 degree = 180 degree

x = 180 -145

x=35 degree

reason = being linear pair

b.40 + x =90 degree

x = 90 - 40

x = 50 degree

reason = being perpendicular

y = x + 40

y = 50 + 40

y = 90 degree

reason = being vertically opposite angles

c.50 + 60 + x=180 degree

110 + x =180

x = 180-110

x = 70 degree

reason = being linear pair

z = 60 degree

reason = being vertically opposite angles

y = 50 degree

reason = being vertically opposite angles

d. x = 80 +10

x =90 degree

reason = being vertically opposite angles

y + x =180 degree

y + 90 =180

y = 180 - 90

y = 90 degree

reason = being linear pair

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°