Question

The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (1/2)∠BAC, then what is the value of ∠BAC ?​

Answer 1

$\huge\sf\red{Given\::}$

• $\sf \angle ACD\: = \:114\degree$
• $\sf \angle ABC\:=\:\dfrac{1}{2}\:\angle BAC$

$\huge\sf\blue{To\:Find\::}$

• $\sf The\: value\: of \:\angle BAC$

$\huge\sf\purple{Solution\::}$

$\sf Let,$

• $\sf \angle ABC \: = \: x$
• $\sf \angle BAC \:=\: 2x$

$\sf\underline{Now,\:By\:using\: exterior\: angle\: property}$

$\longrightarrow\:\:\sf \angle BAC \:=\:\angle ABC \:=\: \angle ACD$

$\longrightarrow\:\:\sf 2x\:+\:x\:=\:144\degree$

$\longrightarrow\:\:\sf 3x\:=\:144\degree$

$\longrightarrow\:\:\sf x\:=\:\dfrac{\cancel{144\degree}}{\cancel{3}}$

$\longrightarrow\:\:\sf x\:=\:38\degree$

$\sf Put \:the\:x\: value\:in\:\angle BAC$

$\longrightarrow\:\:\sf 2\:\times\:38\degree$

$\longrightarrow\:\:\sf 76\degree$

$\sf\star\:\:\underline\pink{Hence, \:\angle BAC\:is\:76\degree}$

Answer 2

Answer:

Given

The side BC of ΔABC is produced to D

∠ACD = 114°

∠ABC= (1/2)∠BAC

Find out

Find the value of ∠BAC

Solution

★ Let the ∠ABC be x and ∠BAC be 2x

**According to exterior angle property**

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

→ ∠BAC + ∠ABC = ∠ACD

→ 2x + x = 114°

→ 3x = 114°

→ x = 114/3

→ x = 38°

Hence,

∠ABC = x = 38°

∠BAC = 2x = 38 × 2 = 76°

Additional Information

★If two parallel lines are cut by a transversal,then

Pairs of corresponding angles are equal

pairs of alternate angles are equal

interior angles on the same side of the transversal are supplementary