Question

ASAP OVERDUE ASSIGNMENT

Answer 1

m∠X = 44°

m∠Y = 74°

m∠Z = 62°

Explanation:

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180°. In other words, if you add up the measures of the three angles inside any triangle, the total will be 180°.

To determine the measure of each angle in the given triangle, we first need to find the value of x. To do this, equate the sum of the three interior angles to 180° and solve for x:

`\begin{aligned}2x^(\circ) + (3x + 8)^(\circ) + (3x - 4)^(\circ) &= 180^(\circ)\\\\2x + 3x + 8 + 3x - 4 &= 180\\\\8x + 4 &= 180\\\\8x + 4-4 &= 180-4\\\\8x &= 176\\\\(8x)/(8) &= (176)/(8)\\\\x &= 22\end{aligned}`

Now, substitute the found value of x into each of the angle expressions:

`\begin{aligned}m \angle X &= 2(22)^(\circ)\\ &= 44^(\circ)\end{aligned}`

`\begin{aligned}m \angle Y &= (3(22) + 8)^(\circ)\\&=(66+8)^(\circ)\\ &= 74^(\circ)\end{aligned}`

`\begin{aligned}m \angle Z &= (3(22) - 4)^(\circ)\\ &= (66 - 4)^(\circ)\\&= 62^(\circ)\end{aligned}`

Therefore, the measure of each angle is:

• m∠X = 44°
• m∠Y = 74°
• m∠Z = 62°

Answer 2

Angle X = 44°

Angle Y = 74°

Angle Z = 62°

Explanation:

Since the sum of the interior angles of a triangle is 180 degrees.

Using this,

We can say that:

`\sf \angle X +\angle Y + \angle Z = 180^\circ`

Substitute the value:

2x° + (3x+8)°+(3x-4)°=180°

Simplify like terms:

8x°+4°=180°

Subtract 4° on both sides:

8x°+4°-4°=180°-4°

8x°= 176°

Divide both sides by 8.

`\sf (8x)/(8)=(176^\circ)/(8)`

x = 22°.

Now,

Angle X = 2x° = 2×22 = 44°

Angle Y = (3x+8)°=(3×22+8)=66°+8°= 74°

Angle Z = (3x-4)°=(3×22-4)= 66°-4°= 62°