Question

Triangle XYZ is shown below.

In the triangle X-Y-Z, the measure of angle X is 'a' degrees, angle Y is '2a' degrees, and angle Z is 'a plus 10' degrees.

Which statement is TRUE?

Responses

The measure of ∠X
= 180° minus the measure of ∠Y
because adjacent angles in a triangle are supplementary.

The measure of ∠ X = 180° minus the measure of ∠ Y because adjacent angles in a triangle are supplementary.

The measure ∠X=60˚
because each angle is equal to a third of the triangle's total angle measure of 180˚.

The measure ∠ X = 60 ˚ because each angle is equal to a third of the triangle's total angle measure of 180˚.

The measure of ∠Y=85˚
because the three angles represent proportional parts of the triangle's total angle measure of 180˚.

The measure of ∠ Y = 85 ˚ because the three angles represent proportional parts of the triangle's total angle measure of 180˚.

The measure of ∠Z=42.5˚
because the sum of the measures of the triangle's three angles total 180˚.

The measure of ∠ Z = 42.5 ˚ because the sum of the measures of the triangle's three angles total 180˚.

Answer 1

The correct statement is: The measure of ∠Y=85˚ because the three angles represent proportional parts of the triangle's total angle measure of 180˚. Here's why this statement is true: In a triangle, the sum of all three angles is always equal to 180°. We are given that angle X is 'a' degrees, angle Y is '2a' degrees, and angle Z is 'a plus 10' degrees. To find the value of 'a', we can set up an equation using the given information: a + 2a + (a + 10) = 180 Combining like terms, we get: 4a + 10 = 180 Subtracting 10 from both sides, we have: 4a = 170 Dividing both sides by 4, we get: a = 42.5 Now that we know the value of 'a', we can find the measure of each angle: ∠X = a = 42.5° ∠Y = 2a = 2(42.5) = 85° ∠Z = a + 10 = 42.5 + 10 = 52.5° Therefore, the measure of ∠Y is indeed 85°, as stated in the correct statement.

Step-by-step explanation:

Answer 2

In triangle XYZ, the angles add up to 180 degrees. The measure of ∠X is found to be 42.5 degrees, ∠Y is 85 degrees, and ∠Z is 52.5 degrees after solving the equation involving their measures given as 'a', '2a', and 'a + 10'. Therefore, none of the provided responses is correct.

Step-by-step explanation:

The question involves understanding the properties of triangles in geometry. Specifically, in triangle XYZ with angles X, Y, and Z, the measure of angle X is 'a' degrees, angle Y is '2a' degrees, and angle Z is 'a + 10' degrees. Given that the sum of the angles in any triangle adds up to 180 degrees, we can write an equation to find the value of 'a' and subsequently the measures of each angle. Applying the equation:

a + 2a + (a + 10) = 180,

We simplify this to:

4a + 10 = 180,

Then, solving for 'a', we get:

4a = 170,

a = 42.5 degrees.

Therefore, using the value of 'a', we can calculate the measure of each angle:

∠X = a = 42.5 degrees,

∠Y = 2a = 2(42.5) = 85 degrees,

∠Z = a + 10 = 42.5 + 10 = 52.5 degrees.

None of the provided responses is correct, so the true statement must be deduced from these calculations.