Question

In the following figure, l || m. Find the measure of ∠ x.

1 point



(a) 60°

(b) 45°

(c) 30°

(d) none of these

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Answer 1

Answer:

(d)none of the these

Step-by-step explanation:

l and m are parallel so there is no angle formed

Answer 2

Note: The figure is missing in the given question, the question figure is attached in the answer.

Given: $l||m$

To find: Find the measure of $\[\angle x\]$.

Solution:

Note that from the question figure, $\[\angle BCD = \left( {2y + {{25}^ \circ }} \right),\angle ECF = \left( {x + {{15}^ \circ }} \right),\angle ABC = 3y\]$.

Find the value of y.

Understand that,

$\[\angle ABC = \angle BCD\]$ (alternate angles)

$\[\begin{array}{l} \Rightarrow 3y = 2y + {25^ \circ }\\ \Rightarrow 3y - 2y = {25^ \circ }\\ \Rightarrow y = {25^ \circ }\end{array}\]$

Find the value of x.

$\[\angle ECF = \angle BCD\]$ (vertically opposite angles)

$\[\begin{array}{l} \Rightarrow x + {15^ \circ } = 2y + {25^ \circ }\\ \Rightarrow x + {15^ \circ } = 2 \times \left( {{{25}^ \circ }} \right) + {25^ \circ }\\ \Rightarrow x + {15^ \circ } = {50^ \circ } + {25^ \circ }\end{array}\]$

$\[\begin{array}{l} \Rightarrow x + {15^ \circ } = {75^ \circ }\\ \Rightarrow x = {75^ \circ } - {15^ \circ }\\ \Rightarrow x = {60^ \circ }\end{array}\]$

Therefore, the measure of $\[\angle x\]$ is $\[{60^ \circ }\]$.

Hence, the correct answer is option (a). i.e., $\[{60^ \circ }\]$.