Question

B
С
Two angles of a triangle are equal and third angle is 80°. Find the measure of equal ang​

Answer 1

Answer:

x+30∘+80∘=180∘  

x+110∘=180∘

x=180∘−110∘

x=70∘

Step-by-step explanation:

Answer 2

${\underline {\boxed {\Large {\bf \gray { {50}^{\circ} } }}}}$

Given:

• Two angles of a triangle are equal.

• Measure of the third angle = 80°

To calculate:

• The measure of equal angles.

Calculation:

Let the measure of each two unknown angles be "x°". Now as we know that,

★ $\small \boxed {\sf { Sum \: of \: interior \: angles \: of \: \triangle = {180}^{\circ} }}$

Now, according to the question :

$\sf { \dashrightarrow {80}^{\circ} + {x}^{\circ} + {x}^{\circ} = {180}^{\circ} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf { \dashrightarrow {80}^{\circ} + {2x}^{\circ} = {180}^{\circ} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf { \dashrightarrow {2x}^{\circ} = {180}^{\circ} - {80}^{\circ} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf { \dashrightarrow {2x}^{\circ} = {100}^{\circ} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf { \dashrightarrow {x}^{\circ} = \dfrac{{100}^{\circ}}{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\boxed{ \sf { \dashrightarrow {x}^{\circ} = {50}^{\circ} }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, measure of each equal angles is 50°.

Verification:

★ $\small \boxed {\sf { Sum \: of \: interior \: angles \: of \: \triangle = {180}^{\circ} }}$

LHS :

→ x° + x° + 80°

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→ 50° + 50° + 80°

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→ 100° + 180°

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→ 180°

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

RHS :

→ 180°

• LHS = RHS

Hence, verified!

______________________________

More about triangles:

• Perimeter = S + S + S or Sum of all sides.
• Area = $\sf {\dfrac{1}{2} bh}$

Properties of triangle :

★ Angle sum property :

• According to this property, sum of all interior angles of triangle is equal to 180°.

★ $\small \boxed {\sf { Sum \: of \: interior \: angles \: of \: \triangle = {180}^{\circ} }}$

★ Exterior angle property :

• According to this property, sum of two interior opposite angles of triangle is equal to measure of exterior angle.

★ $\small \boxed {\sf { Sum \: of \: two \: interior \: opposite\: angles \: of \: \triangle = Exterior \: angle }}$