Question

Find the value of x and y​

Answer 1

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Answer 2

Find the value of unknown 'x' and 'y'.

$\boxed { \huge \bf { First \: Part } }$

Here, in this question given that:–

• One interior angle measurement = 35°

• Exterior angle = 62°

To find the value of x :

We know that,

• Vertically opposite are equal if two angles intersect.

$\boxed { \large \bf \red { \therefore x = {62}^{\circ} } }$ [ Vertically opposite]

To find the value of y :

Angle sum property of triangle :–

In the beginning of the solution, we got the value of 'x',

• Sum of the interior angles of a triangle = 180°

$\rm { \therefore {35}^{\circ} + {62}^{\circ} + y = {180}^{\circ} }$

$\rm { \implies {97}^{\circ} + y = {180}^{\circ} }$

$\rm { \implies y ={180}^{\circ} - {97}^{\circ} }$

$\boxed { \large \bf \red { y = {83}^{\circ} } }$

$\boxed { \huge \bf { Second \: Part } }$

Here, the given triangle is isosceles triangle. We know that,

• If the two lines are equal then their angles will also be equal.

• Vertically opposite are equal if two angles intersect.

So,

• One interior angle measurement = 80° [ Vertically opposite]

Now,

$\rm { \implies {80}^{\circ} + x + x = {180}^{\circ} }$ [ Angle sum property of triangle]

$\rm { \implies {80}^{\circ} + 2x={180}^{\circ} }$

$\rm { \implies 2x={180}^{\circ} - {80}^{\circ} }$

$\rm { \implies 2x= {100}^{\circ} }$

$\rm { \implies x= \dfrac{{100}^{\circ} }{2} }$

$\boxed { \large \bf \red { x ={50}^{\circ} } }$

Also,

$\rm { \implies {x}^{\circ} + {80}^{\circ} = y }$ [ Exterior angle property of triangle]

$\rm { \implies {50}^{\circ} + {80}^{\circ} = y}$

$\boxed { \large \bf \red { y = {130}^{\circ} } }$

_____________________________________

D) Find the value of unknown 'x'

$\implies$ Since the triangle is right angle triangle we can apply here the Pythagoras property.

Given:

• Base (B) = 15cm

• Perpendicular (P) = 8cm

To find :

• Hypotenuse (H or x ) = ?

Calculation:

We know that,

$\boxed { \large \bf { {(H)}^{2}= {(B)}^{2} +{(P)}^{2} } }$

Substituting the values:

$\rm { \implies {x}^{2}= {25}^{2} +{8}^{2} }$

$\rm { \implies {x}^{2}= 225 +64}$

$\rm { \implies {x}^{2}= 289 }$

$\rm { \implies x = \sqrt{ 289} }$

$\boxed { \large \bf \red { x = 17 cm } }$