Question

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Answer 1

Answer:

1.$x^\circ= 7^\circ$

2.(a)Therefore , Side LJ =side CA

(b) BC = KL

Step-by-step explanation:

1.

we know that, vertically opposite angles are congruent .

$\therefore (x+16)^\circ= (4x-5)^\circ$

$\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ$

$\Leftrightarrow 3x^\circ= 21^\circ$

$\Leftrightarrow x^\circ= 7^\circ$

2.

(a)SAS = side,angle , side

Given ,side AB = side KJ

and ∠CAB= ∠LJK

All Pythagorean Triples are unique.

Since side AB = side KJ

Therefore , Side LJ =side CA

It satisfies SAS postulate ThereforeΔABC≅ΔKJL

(b)

HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.

Since,

All Pythagorean Triples are unique.

Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL