Question

find X and Y in the following​

Answer 1

Answer:

The 3 angles of a equlateral traingle of 60°

Step-by-step explanation:

X=60°

Y

60+y = 180

y = 180-60

y=120

Answer 2

Given:

• The triangle is equilateral

To Find:

• the measure of $\bf{\green{x \:and\:y}}$

Solution:

➪ Since the triangle is equilateral so all its angles measure the same.

$\purple{ \mathfrak{ \underline{As \: we \: know \: that : }}}$

${ \orange{ \dashrightarrow \sf \: sum \: of \: interior \: angles \: in \: a \: triangle = 180 \degree}}$

So, let's find the measure of the angles:

→ we consider each angle of the triangle as n

$\longrightarrow \sf \: n + n + n = 180 \\ \\ \\ \longrightarrow \sf 3n = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: n = \cancel\frac{180}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf {\orange{\: n = 60 \degree \bigstar}} \: \: \: \: \: \: \: \: \: \: \:$

❶ hence, each angle in the triangle measures 60°.

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◕ Now, let's find angle x

→ angle x is the exterior angle of angle 60°

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ sum \: of \:interior \: and \: exterior \: is \: 180 \degree}}}}}$

➪$\rm {\purple{ x+60 = 180}}$

➪$\rm {\purple{ x = 180-60}}$

➪ $\bf{\green{X = 130\degree}}$

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◕Now, let's find angle y

→ angle y and 60° are vertically opposite angles

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ vertically \: opposite \: angles \: are \: equal}}}}}$

➪$\bf {\gray{ Y = 60\degree}}$

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More to know:

• A triangle has three sides and three angles.

• The sum of the angles of a triangle is always 180 degrees.

• The exterior angles of a triangle always add up to 360 degrees.

• The sum of consecutive interior and exterior angle is supplementary.

hope this helps.!