Question

Find the measures of angles LA = (3y + 4)° and ZB = (5y - 5)º, if their sum is 120°.​

Answer 1

$\bigstar \: \boxed{\sf{\color{purple}{Answer:}}}$

GIVEN :-

Let ABCD be a cyclic quadrilateral.

∠A=2x+4,∠B=y+3,∠C=2y+10,∠D=4x−5

In cyclic quadrilateral the sum of the opposite

angles in 180°.

Therefore,

∠A+∠C=180°

⇒2x+4+2y+10=180°

⇒2x+2y=166°

⇒2x+2y=166°⇒x+y=83°

→1

→1∠B+∠D=180•

⇒y+3+4x−5=180°

⇒y+3+4x−5=180°⇒4x+y=182°→2

Solving 1 and 2, we get

4x+y−x−y=182°−83°⇒3x=99°⇒x=33°

4x+y−x−y=182°−83°⇒3x=99°⇒x=33°& 33°+y=83°⇒y=83°−33°=50°

∴∠A=2×33°+4=70°,∠B=50°+3=53°

∴∠A=2×33°+4=70°,∠B=50°+3=53°∠C=2×50°+10=110°,∠D=4×33°−5=127°

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