Question

1. a 9 ft 48° 48° b m∠a = ac = 12. m n p m∠p = m∠n = m∠m =

Explanation:

Step1: Find angle A in first triangle

Sum of angles in a triangle is 180°. So $m\angle A=180^{\circ}- 48^{\circ}-48^{\circ}=84^{\circ}$.

Step2: Find side AC in first triangle

Since two angles ($\angle B = \angle C=48^{\circ}$) are equal, the triangle is isosceles. So $AC = AB = 9$ ft.

Step3: Find angles in second triangle

In $\triangle MNP$, since $MP = NP$, it is isosceles. Let $m\angle M=m\angle N$. Using angle - sum property of a triangle ($m\angle M + m\angle N+m\angle P=180^{\circ}$). Let $m\angle M = m\angle N = x$. Then $2x + m\angle P=180^{\circ}$. But we don't have enough information about angles in $\triangle MNP$ from the given figure to find exact values of angles other than the isosceles - angle relationship. However, if we assume the marks on the sides imply equal - side lengths, and we know the angle - sum property of a triangle.

Answer:

$m\angle A = 84^{\circ}$, $AC = 9$ ft, $m\angle M=m\angle N$, $m\angle P=180^{\circ}-2m\angle M$ (more information needed for exact numerical values of angles in $\triangle MNP$)