Question

one angle of a triangle is 80.the other 2 angles are in the ratio of 13:7. Find the angles

Answer 1

☆ Given :

• Measure of one angle of a triangle is 80°
• The ratio of other two angles are in ratio 13 : 7

☆ To find :

• The angles of the triangle

☆ Solution :

The first angle of the ∆ is 80° (Given)

Let the second angle of ∆ be 13x

And the third angle of ∆ be 7x

Now,we know that :

• ★ Sum of all angles of triangle = 180°

(Angle sum property of triangle)

A/Q

⟼ 80° + 13x + 7x = 180°

⟼ 80° + 20x = 180°

⟼ 20x = 180° - 80°

⟼ 20x = 100°

⟼ x = 100/20

⟼ x = 5

Therefore,

• The measure of second angle of ∆ (13x) = 13×5 = 65°
• The measure of third angle of ∆ (7x) = 7×5 = 35°

Check :

We know :

Sum of all angles of ∆ = 180°

=> 80° + 13x + 7x = 180°

Putting the value :

→ 80° + 65° + 35° = 180°

→ 145° + 35° = 180°

→ 180° = 180°

Hence, both sides are equal.

Thus, checked !

Answer 2

Step-by-step explanation:

Given: Measure of one angle of a triangle is 80°. The other two angles are in the ratio of 13 : 7.

Need to find: Angles of triangle ?

❏ Let the second angle of triangle be 13x and the third angle of triangle be 7x.

‎

__________________

‎

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

‎

$\star\;\boxed{\sf{\pink{Sum\ of\ all\ angles\ of\ \triangle\ =\ 180^{\circ}.}}}$

‎

$\bf {Here} \begin{cases} &\sf{First\ angle\ =\ 80^{\circ}.} \\ &\sf{Second\ angle\ =\ 13x.} \\ &\sf{Third\ angle\ =\ 7x.} \end{cases}$

‎

Therefore,

‎

$\sf : \implies {80\ +\ 13x\ +\ 7x\ =\ 180} \\ \\ \\ \sf : \implies {80\ +\ 20x\ =\ 180} \\ \\ \\ \sf : \implies {20x\ =\ 180\ -\ 80} \\ \\ \\ \sf : \implies {20x\ =\ 100} \\ \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{100}{20}} \\ \\ \\ \sf : \implies {\underline{\fbox{\purple{\bf x\ =\ 5.}}}}\bigstar$

‎

Hence,

‎

• Second angle = 13x = 13 × 5 = 65°.
• Third angle = 7x = 7 × 5 = 35°.

‎

$\sf \therefore {\underline{The\ required\ angles\ are\ \bf 65^{\circ}\ \sf and\ \bf 35^{\circ}.}}$

‎

⠀⠀⠀

$\begin{gathered}\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar Verification \bigstar}}}}}\mid}\\\\\end{gathered}\end{gathered}$

‎

$\sf {Sum\ of\ all\ angles\ of\ \triangle\ =\ 180^{\circ}}$

$\sf : \implies {80^{\circ}\ +\ 65^{\circ}\ +\ 35^{\circ}\ =\ 180^{\circ}}$

$\sf : \implies {145^{\circ}\ +\ 35^{\circ}\ =\ 180^{\circ}}$

$\sf : \implies {\underline{\boxed{\purple{\bf 180^{\circ}\ =\ 180^{\circ}.}}}}\bigstar$