Question

The measures of angles of a triangle are (x - 5)°, (x + 15)° and (2x - 30)°. Find all the angles.​

Answer 1

Given: The measure of angles of triangle are (x - 5)°, (x + 15)° and (2x - 30)°.

Need to Find: Angles of triangle?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

$\underline{\dagger\; \frak{As\; we\; know\; that\; :}}$

• ASP (Angle Sum ProPerty) of the triangle States that sum of all angles of a triangle is 180°.

⠀

$\\:\implies\quad\sf{(x-5)+(x+15)+(2x-30)={180}^{\circ}}$

⠀

$\\:\implies\quad\sf{x-5+x+15+2x-30={180}^{\circ}}$

⠀

$\\:\implies\quad\sf{4x-{20}^{\circ}={180}^{\circ}}$

⠀

$\\:\implies\quad\sf{4x={180}^{\circ}+{20}^{\circ}}$

⠀

$\\:\implies\quad\sf{4x={200}^{\circ}}$

⠀

$\\:\implies\quad\sf{x=\cancel{\dfrac{{200}^{\circ}}{4}}}$

⠀

$\\:\implies\quad\pmb{\sf{x={50}^{\circ}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Therefore,

• x - 5 = 50 - 5 = 45
• x + 15 = 50 + 15 = 65
• 2x - 30 = 2(50)-30 = 70

⠀

$\\\underline{\therefore\sf{Hence,\: the\: angles\: of\: \triangle\: are}\: \bold{{45}^{\circ}\: {65}^{\circ}}\: \sf{and}\: \bold{{70}^{\circ}\sf{respectively.}}}$