Question

Sum of two angles of a triangle is 90degree . Find the third angle . What type of triangle is this ?

Answer 1

AnswEr:-

❀ Your answer is 90° And it is a right angled triangle.

ExplanaTion:-

Given:-

• Sum of two angles of a triangle is 90°.

To Find:-

• The measure of third angle.

• Let the three angles of the triangle be x, y and z and the angle which we have to find is x.

Concept Used:-

• Angle Sum Property Of a Triangle:- Sum of all interior angles of a triangle is always equal to 180°.

Now,

Here measure of two angles is 90° and the third angle is x which we have to find.

Therefore,

↦ x + y + z = 180°.

↦ x + 90° = 180°.

[As sum of two angles is 90°].

↦ x = 180° - 90°.

↦ x = 90°.

Now we have to find out the type of triangle it is:-

So above we have find out the value of third angle which is 90°.

Therefore it is a right angled triangle because we know that if any one angle of a trianlge would be 90° then it is called as right angled triangle and here also measure of one angle (x) is 90° hence it is a right angled triangle.

Answer 2

Answer:

$\textsf{Let the \angle A, \angle B and \angle C are the given}\\ \textsf{angles of the \Delta ABC.} \\\\\textsf{Here ; we have}</p><p>\\\\\textsf{Sum of Two Angles of Triangle is 90 ^{\circ} }\\ \bullet\:\:\sf\measuredangle(A + B) = 90^{\circ}$

⠀⠀⠀$\rule{160}{1}$

☢ $\underline{\textsf{According to the Question :}}$

$\dashrightarrow\sf\:\:Sum\:of\:all\:angles\:of\: Triangle=180^{\circ}\\\\\\\dashrightarrow\sf\:\:\angle\:A+\angle\:B+\angle\:C=180^{\circ}\\\\\\\dashrightarrow\sf\:\:90^{\circ} + \angle\:C = 180^{\circ}\\\\\\\dashrightarrow\sf\:\:\angle\:C = 180^{\circ} - 90^{\circ}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf \angle\:C = 90^{\circ}}}$

⠀

$\therefore\:\underline{\textsf{Hence, Measure of the third Angle is \textbf{90 ^{\circ} }}}.$

$\rule{200}{1.7}$

⠀⠀⠀⠀⠀⠀Type of Triangle

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.4mm}\qbezier(8,2.3)(8.3,2.3)(8.4,2.6)\put(7.7,1){\large\sf{C}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.4,2.3){\vector(1, - 1){.4}}\put(9.7,1.3){\vector( -2,1){.5}}\put(7.7,2.7){\sf{\large{A}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\qbezier(9.8,1)(9.7,1.25)(10,1.4)\put(8.8,1.6){\sf\large{90^{\circ} }}\end{picture}$

⠀

As we found that Measure of Third Angle i.e. $\sf \angle\:C = 90^{\circ}$ , & we know that If Measure of any Angle is equal to 90° then that Triangle is Right Angle Triangle.

⠀

$\therefore\:\underline{\textsf{Hence, Given triangle is \textbf{Right Angle Triangle}}}.$