Question

Find the value of x. ​

Answer 1

Answer:

Step-by-step explanation:

We know that,

according to the angle sum property, the angles of a triangle are supplementary.

angleA+angleB+angleC=180 degrees

x + 70 + 65 =180

x + 135=180

x = 45 degrees

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Answer 2

Given Information:

• Measures of the interior angles :

$\sf{ \longrightarrow \: \angle \: A = x} \\ \\ \sf{ \longrightarrow \: \angle \: B = {70}^{ \circ} } \\ \\ \sf{ \longrightarrow \: \angle \: C = {65}^{ \circ} }$

Solution:

We have to calculate the measure of angle A or value of x. So, here we can find the value of x by forming a suitable equation.As we know that, sum of the interior angles of the triangle is equal to 180°. So,

$\sf{ \longrightarrow \: \angle \: A + \angle \: B + \angle \: C ={180}^{ \circ} } \\ \\ \\ \sf{ \longrightarrow \: x + {70}^{ \circ} + { 65}^{ \circ} ={180}^{ \circ} } \\ \\ \\ \sf{ \longrightarrow \: x + { 135}^{ \circ} ={180}^{ \circ} } \\ \\ \\ \sf{ \longrightarrow \: x ={180}^{ \circ} - { 135}^{ \circ} } \\ \\ \\ \longrightarrow \: \underline{ \boxed{ \sf{x ={ 45}^{ \circ} }}} \: \red{ \bigstar}$

Henceforth, value of x is 45°.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \sf Verification} \\ \\ \sf{ \longrightarrow\angle A + \angle B + \angle C = {180}^{\circ} } \\ \\ \\ \sf{ \longrightarrow \:{45}^{\circ} + {70}^{\circ} + {65}^{\circ}= {180}^{\circ} } \\ \\ \\ \sf{ \longrightarrow \:{180}^{\circ} = {180}^{\circ} }$

Hence, verified!!

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More Information :

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

• $\sf { \dfrac{1}{2} \times Base \times Height }$

★ Area of an equilateral triangle:

• $\sf { \dfrac{\sqrt{3}}{4} \times {Side}^{2} }$

★ Area of a triangle when its sides are given :

• $\sf { \sqrt{s[ (s-a)(s-b)(s-c) ]} }$

Where,

S= Semi-perimeter or $\sf {\dfrac{a+b+c}{2} }$