Question

In the given figure, l || m. Find the value of x.
angle a is 52⁰ and angle b is 43⁰
​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=95\degree}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given:}} \\ \tt: \implies CL|| DM\\ \\ \tt: \implies \angle DBO = 43 \degree \\ \\ \tt: \implies \angle CAO = 52 \degree \\ \\ \red{ \underline \bold{To \: Find:}} \\ \tt: \implies \angle AOB =?$

• According to given question :

$\tt \circ \: Let \: a \: line \: bisecting \: \angle \: AOB \: and \\ \tt \: \: \: line \: parallel \: to \: line \: CL \: and \: DM \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies \angle CAO= \angle AOF\: \: \: \: \: (Alternate \: angle) \\ \\ \tt: \implies 52 \degree = \angle AOF \\ \\ \green{\tt: \implies \angle AOF= 52 \degree} \\ \\ \bold{Similarly : } \\ \tt: \implies \angle DBO = \angle BOF \: \: \: \: \: (Alternate \: angle) \\ \\ \tt: \implies 43 \degree = \angle BOF$

$\green{\tt: \implies \angle BOF = 43 \degree} \\ \\ \bold{For \: finding \: value } \\ \tt: \implies \angle AOB= \angle AOF + \angle BOF\\ \\ \tt: \implies x = 52 \degree + 43 \degree \\ \\ \green{\tt: \implies x = 95 \degree} \\ \\ \green{\tt \therefore Value \: of \: x \: is \: 95 \degree}$

Answer 2

Answer:

✍Given:

✏CL∣∣DM

✏∠DBO=43°

✏∠CAO=52°

✍ToFind:

✏∠AOB=?

✍ ATQ:-

✏ Let a line bisecting ∠AOB and line parallel to line CL and DM

➡ As we know that,

✏∠CAO=∠AOF(Alternate angle)

=> 52° = ∠AOF

=> ∠AOF = 50°

➡ Similarly,

=> ∠DBO = ∠BOF ( alternate angle)

=> 43° = ∠BOF

=> ∠BOF = 43°

➡ Finding the values:-

=> ∠AOB = ∠AOF + ∠BOF

=> x = 52° + 43°

=> x = 95°

✍ Hence, the value of x is 95°