Question

In the given figure if AB | DE, angleBAC = 35digree and
angleCDE=53º, find angleDCE.
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Answer 1

Given:-

• AB \\ DE
• <BAE = 35⁰
• <CDE = 53⁰

To find:-

• <DCE

properties to be used:-

• alternate interior angles
• angle sum property of triangle

Solution:-

$\implies$ <BAE = <CED (by alternate interior angles)

$\implies$ <CED = 35⁰

$\implies$ <CED + <CDE + <DCE = 180⁰ (by angle sum property of triangle)

$\implies$ 35⁰+53⁰+<DCE = 180⁰

$\implies$ <DCE + 88⁰ = 180⁰

$\implies$ <DCE = 92⁰

Answer 2

Answer:

BAC = DEC = 35 DRGREE ( ALTERNATE INTERIAL ANGLES )

NOW

IN TRIANGLE DCE

ANGLE D +C+E = 180 DEGREE ( SUM ANGLE PROPERTY OF A TRIANGLE )

C+ 53 + 35 =180

C = 180 - 88

C = 92 DEGREE

c = DCE = 92 DEGREE