Question

Find the value of x and the measure of angle BON. please​

Answer 1

Answer:

x=40°

Angle BON =140°

Step-by-step explanation:

Given-

Angle K=115°

Angle L=75°

PINK and BLUE are parallelograms

To Find-

1) x

2)Angle BON

Calculations-

Angle K=115° [Given]

Angle K + Angle KNI=180° [In a ||gm Corresponding Angles are supplementary]

⇒115°+Angle KNI=180°

⇒Angle KNI=180°-115°

⇒Angle KNI=65°

Angle L=Angle UEB [In a ||gm opposite angles are equal]

⇒Angle UEB=75°

In ΔENO

Angle UEB+ Angle KNI+x=180° [Angle sum property of a Δ]

⇒75°+65°+x=180°

⇒140°+x=180°

⇒x=180°-140°

⇒x=40°

Therefore, x=40°

Angle BON +x=180° [Linear pair]

⇒Angle BON +40°=180°

⇒Angle BON =180°-40°

⇒Angle BON =140

Therefore, Angle BON =140°