Question

one of the angles of a triangle is 110 and the other two angles are equal .what is the measures of each of these equal angles​

Answer 1

• Measure of each of equal angles is 35°.

Step-by-step explanation:

Given:-

• One angle of triangle is 110°.
• Other two angles are equal.

To find:-

• Measure of each equal angles.

Solution:-

Let, Other two angles be x and x.

We know sum of all angles of triangle is 180°.

So,

$\longrightarrow$ x + x + 110° = 180°

$\longrightarrow$ 2x + 110° = 180°

$\longrightarrow$ 2x = 180° - 110°

$\longrightarrow$ 2x = 70°

$\longrightarrow$ x = 70°/2

$\longrightarrow$ x = 35°

Verification:-

$\longrightarrow$ x + x + 110° = 180°

• Put x = 35°

$\longrightarrow$ 35° + 35° + 110° = 180°

$\longrightarrow$ 180° = 180°

$\boxed{\sf Hence \: Verified.}$

We take x be equal angles.

Therefore,

Measure of each of equal angles is 35°.

Answer 2

Given:

• One of the angles of a triangle is 110°.

⠀⠀⠀

To find:

• Measure of other two equal angles?

⠀⠀⠀

Solution:

⠀⠀⠀

$\setlength{\unitlength}{1.1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)( - 0.3,3)\qbezier(5,0)(5,0)( - 0.3,3)\qbezier(5,0)(1,0)(1,0)\put( - 0.5,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\qbezier(4.18,0.5)(3.9,0.25)(4,0)\qbezier(0.8,0.5)(1.4,0.3)(1.5,0)\qbezier( - 0.05,2.4)(0.1,2.2)(0.5,2.5)\put(0.4,2.1){ \sf x }\put(1.4,0.4){ \sf 110^\circ }\put(3.6,0.25){ \sf x }\end{picture}$

☯ Let other two equal angles be x and x.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

• Sum of all angles of a triangle is 180°.

⠀⠀⠀

$\bigstar\:{\underline{\sf{Now,\:In\; \triangle\: ABC\::}}}$

$:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ$

$\sf Here \begin{cases} & \sf{\angle\:A = \bf{x}} \\ & \sf{\angle\:B = \bf{x}} \\ & \sf{\angle\:C = \bf{110^\circ}}\end{cases}$

$\dag\;{\underline{\frak{Putting\:values,}}}$

$:\implies\sf x + x + 110^\circ = 180^\circ$

$:\implies\sf 2x + 110^\circ = 180^\circ$

$:\implies\sf 2x = 180^\circ - 110^\circ$

$:\implies\sf 2x = 70^\circ$

$:\implies\sf x = \cancel{ \dfrac{70^\circ}{2}}$

$:\implies{\underline{\boxed{\sf{\purple{x = 35^\circ}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Measure\:of\:other\:two\:equal\: angles\:of\:a\:triangle\:is\: \bf{35^\circ}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\star\;{\underline{\sf{Types\:of\:triangle,}}}$

• Equilateral triangle: An equilateral triangle has three equal sides and angles. All angles of an equilateral triangle are of measure 60°.

• Isosceles triangle: An isosceles triangle have two equal sides and two equal angles or with two acute angles and one obtuse angle.

• Scalene triangle: A scalene triangle has three different angles and none of its sides are equal in length.

• Right angled triangle: A right-angled triangle has one 90° angle.

• Obtuse triangle: An obtuse triangle has three different sides and angles, with one angle greater than 90°.