Question

Geometry homework help, please show all of your work.

Questions 3: ∆ABC ~ ∆DEF. If ∠A=70° and ∠F=60°, what is the measure of ∠B? Show all work.

Answer 1

The answer of 1 ques is x=12 units and y=8 units.

The answer of 3 ques is ∠B=50°

Explanation:

Given the triangle JMN in which ΔJKL and ΔJMN are similar

therefore, we can write

`(JK)/(JM)=(JL)/(JN)=(KL)/(MN)`

`(4)/(y-2+4)=(8)/(12)=(x)/(30)`

⇒
`(4)/(y+2)=(8)/(12)` and
`(8)/(12)=(x)/(30)`

⇒
`20=2y+4`
`x=(2* 30)/(5)`

⇒
`2y=16`
`x=12units`

⇒
`y=8units`

In next question of camps.

Part A: Given the two angles ∠ABC and ∠CDE are equal each 90°. As these are alternate angles and are equal hence, both lines AB and DE are parallel.

Part B: Additional angles of pairs ∠BAC and ∠CED, ∠ACB and ∠DCE are equal as first pair is of alternate angles and second pair is vertically opposite angle.

Part C: All the 3 angles of both triangles ΔACB and ΔECD are equal hence, by AAA similarity postulate or we can say by AA similarity postulate both triangles are similar.

Part D: Length of DE is

As the triangles are similar therefore their corresponding sides are proportional

`(BC)/(CD)=(AB)/(DE)\\ \\(3)/(6)=(4)/(x)\\ \\x=8m`

Questions 3: ∆ABC ~ ∆DEF. If ∠A=70° and ∠F=60°, we have to find the measure of ∠B.

As, the triangles are similar corresponding angles are congruent ∴ ∠C=60°

By angle sum property of triangle

∠A+∠B+∠C=180°

⇒ 70°+∠B+60°=180°

⇒ ∠B=50°