Question

two angles of a triangle measure 90 and 30 then the measure of third agle​

Answer 1

Answer:

Step-by-step explanation:

Let a triangle ABC, such that

∠A=90  ∘  ,∠B=30  ∘

 

Now,

∠A+∠B+∠C=180  ∘

⇒90  ∘  +30  ∘  +∠C=180  ∘

⇒∠C=180−120

∴∠C=60  ∘

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Underst \: and \: Concept!}}}$

Here, we have give two angles of a triangle and have to find its third angle. So, as per angle sum property sum of all its angles is 180° and we, have to angles given So, subtract the sum of two angles given by 180° we will get our required answer.

$\huge{\boxed{\sf AnSwer}}$

___________________________

$\huge\underline{\textbf{Given:-}}$

• Two angles of Triangle = 90° and 30°

$\huge\underline{\textbf{Find:-}}$

• Third angle of Triangle.

$\huge\underline{\textbf{Solution:-}}$

$\boxed{\sf Sum \:all\: angles = 180^{\circ}} \qquad \bigg\lgroup \sf Angle\:Sum\:property\bigg\rgroup$

$\implies\sf a + b + c = 180^{\circ}$

$\sf where \small{\begin{cases} \sf a = {90}^{ \circ} \\ \sf b = {30}^{ \circ} \end{cases}}$

$\bigstar\underline{\textsf{Substituting these values:}}$

$\dashrightarrow\sf a + b + c = 180^{\circ}$

$\dashrightarrow\sf {90}^{ \circ} + {30}^{ \circ} + c = 180^{\circ}$

$\dashrightarrow\sf {120}^{ \circ} + c = 180^{\circ}$

$\dashrightarrow\sf c = 180^{\circ} - {120}^{ \circ}$

$\dashrightarrow\sf c = 60^{\circ}$

$\underline{\boxed{\therefore\textsf{Third angle of Triangle is} \: \mathsf{{60}^{ \circ}} }}$