Question

In triangle XYZ, m∠X = 30°, and all the angles have measures that are whole numbers. Angle Y is an obtuse angle. What is the greatest possible measure that angle Z can have?

Answer 1

3 angles: 180°, angle y is 91°, ∠Z is 59°

Step-by-step explanation:

An obtuse angle is an angle whose measure is greater than 90°, but less than 180°.

Write an equation.

m∠X + m∠Y + m∠Z = 180° The sum of the angle measures in a triangle is 180°.

30° + 91° + m∠Z = 180° Substitute values. The least possible measure that obtuse angle Y can have is 91°.

Solve the equation to find m∠Z.

30° + 91° + m∠Z = 180° 132° + m∠Z = 180° Combine like terms.

− 132° − 132° Subtract 132° from both sides. m∠Z = 59°

The greatest possible measure of ∠Z is 59°.

Answer 2

An obtuse angle is over 90 degrees.

So,

All the angles of a triangle add up to 180 degrees.

180-30= 150

The obtuse angle has to be over 90, so the smallest it can be is 91 degrees.

150-91= 59

The largest angle Z can be is 59 degrees.

I hope this helps!
~kaikers