Question

If you could help me with this i would be very thankful

Answer 1

Δ QRS is an obtuse triangle ⇒ according to its angle

Δ QRS is an isosceles triangle ⇒ according to its sides

Explanation:

In Δ QRS

∵ m∠Q = 8x - 17

∵ m∠R = 19x + 4

∵ m∠S = 5x + 1

→ The sum of the interior angles of a Δ is 180°

∴ m∠Q + m∠R + m∠S = 180°

→ Substitute their values in the equation above

∵ 8x - 17 + 19x + 4 + 5x + 1 = 180

→ Add the like terms

∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180

∴ 32x + (-12) = 180

∴ 32x - 12 = 180

→ Add 12 to both sides

∵ 32x - 12 + 12 = 180 + 12

∴ 32x = 192

→ Divide both sides by 32

∵
`(32x)/(32)` =
`(192)/(32)`

∴ x = 6

→ Substitute the value of x in each measure of angles to find them

∵ m∠Q = 8(6) - 17 = 48 - 17

∴ m∠Q = 31°

∵ m∠R = 19(6) + 4 = 114 + 4

∴ m∠R = 118°

∵ m∠S = 5(6) + 1 = 30 + 1

∴ m∠S = 31°

∵ m∠R > 90°

∴ ∠R is an obtuse angle

∴ Δ QRS is an obtuse triangle

∵ m∠Q = m∠S

→ In any Δ if two angles are equal in measures, then the two sides

opposite to these angles are equal in length and the Δ is isosceles

∴ RQ = RS

∴ Δ QRS is an isosceles triangle