1 Answer

Kryptonkal · Answer 1 · 2022-12-30T20:42:51+0000

Consider the below figure attached with this question.

Given:

A, B & C lie on a straight line. D, C & E lie on a different straight line.

$\angle y=117^\circ,\angle z=63^\circ$

To find:

The value of x.

Solution:

A, B & C lie on a straight line.

$m\angle ABD+m\angle DBC=180^\circ$ (Linear pair)

$y+m\angle DBC=180^\circ$

$m\angle DBC=180^\circ-y$

According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of two opposite interior angles.

$m\angle DBC+m\angle BDC=m\angle BCE$ (Exterior angle theorem)

$180^\circ-y+z=x$

$180^\circ-117^\circ +63^\circ =x$

$126^\circ =x$

Therefore, the value of x is 126 degrees.

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