Question

Complete.

$△\mathbf{CAP}$and$△\mathbf{TAP}$ are equilateral and coplanar.$\overline{\mathrm{AP}}$ is a common side of the two triangles.$\mathbf{m}\angle \mathbf{CAT}=\underset{\_}{?}$ (numerical answer).

Short answer

The complete statement is: $△CAP$and $△TAP$are equilateral and coplanar.$\overline{AP}$ is a common side of the two triangles. $m\angle CAT=\mathbf{120}\mathbf{°}$.

Step-by-step solution

- Draw the diagram.

The diagram showing the given situation is:

- Description of step.

The equilateral triangle is a triangle in which all the three sides of the triangle are equal and all the angles are of the measure$60°$ .

As, the triangle$△CAP$is equilateral, therefore, in the triangle ,$△CAP$.

$\angle CAP=\angle APC=\angle PCA=60°$

As, the triangle$△TAP$is equilateral, therefore, in the triangle ,$△TAP$.

$\angle TAP=\angle APT=\angle PTA=60°$

From the diagram it can be noticed that:

$\angle CAT=\angle CAP+\angle TAP$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle CAT=\angle CAP+\angle TAP\\ =60°+60°\\ =120°\end{array}$

Therefore, the measure of the angle$\angle CAT$ is$120°$ .

- Write the complete statement.

Therefore, the complete statement is: $△CAP$and $△TAP$are equilateral and coplanar.$\overline{AP}$ is a common side of the two triangles.$m\angle CAT=120°$ .