91Ó°ÊÓ

If \(x\) exceeds \(y\) by 5 and \(y\) exceeds \(z\) by \(3,\) how is \(x\) related to \(z ?\)

If \(x\) is twice \(y\) and \(y\) is three times \(z,\) how is \(x\) related to \(z ?\)

Given: \(A B>B C, B C>A C\) Prove: \(\mathrm{B}\) is the smallest angle in \(\triangle \mathrm{ABC}\). CAN'T COPY THE GRAPH

The complement of an angle is smaller than the angle. Find the restrictions on the measure of the original angle.

Given: \(\square\) WXYZ, \(\mathrm{XZ}>\mathrm{WY}\) Prove: \(\mathbf{a}<\mathrm{XWZ}>\angle \mathrm{WZY}\) (Use a two-column proof.) b \(\angle \mathrm{XWZ}\) is obtuse. (Use a paragraph proof.)

The sides of a triangle are \(14,6,\) and \(x .\) Find the set of possible values of \(x .\)

Vertex angle A of isosceles triangle ABC is between \(40^{\circ}\) and \(88^{\circ} .\) Find the possible values for \(\angle \mathrm{B}\).

a What is the relation between an exterior angle of a triangle and the two remote interior angles? b What, then, is the relation between an exterior angle and one of the remote interior angles?

A stick \(8 \mathrm{cm}\) long is cut into three pieces of integral lengths to be assembled as a triangle. What is the length of the shortest piece?

If \(x\) exceeds \(y\) by \(20 \%\) and \(y\) exceeds \(z\) by \(20 \%,\) by what percentage does \(x\) exceed z?