Question

Need help asap !!!!!

Answer 1

The answer is x = 5.

Explanation:

Given:

Δ ABC is an Isosceles triangle with AB = CA

m∠ ABC = ( 6x + 4 )°

m∠ BAC = 73°

m∠ BCA = ( 8y - 7 )°

To Find:

x = ?

Solution:

Properties of an Isosceles Triangle.

1. Base angles or two angles are equal.
2. Any two sides are equal.

Here , Δ ABC is an Isosceles triangle with AB = CA

∴ m∠ BAC = m∠ BCA

`73= 8y-7\\8y=73+7\\8y=80\\y=(80)/(10) \\y=10`

∴ m∠ BCA = ( 8y - 7 )°

= 8 × 10 - 7

m∠ BCA = 73 Which is same as ∠ CAB

Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.

`\angle ACB + \angle CAB + \angle CBA = 180`

Substituting the values we get,

`73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=(30)/(6) \\x=5\\`

The answer is x = 5.