Question

section 12.1.12.2 cfu
integrated math 2 - version d

1. classify the following triangle by its sides and angles.

(triangle with angles 73°, 62°, 45° and sides 2.4, 3, 3.2)

1. find the value of x.

(right triangle with angles (2x - 2)°, (x + 5)° and right angle)

1. in the figure, δmnp ≅ δtus. find the value of x and y.

(δmnp with angles 142°, 24° and side (2x - y) m; δtus with side 13 m and angle (2x - 50)°)

Explanation:

Step1: Classify triangle by sides/angles

All sides (2.4, 3, 3.2) are distinct, so scalene. All angles (45°, 62°, 73°) are acute (<90°), so acute.

Step2: Solve for x (right quadrilateral)

Sum of quadrilateral angles = 360°. Right angle = 90°.
$$90 + (2x-2) + (x+5) + 90 = 360$$
Simplify: $3x + 183 = 360$ → $3x = 177$ → $x = 59$

Step3: Solve for x (congruent triangles)

Corresponding angles of congruent triangles are equal: $\angle U = \angle P = 24^\circ$
$$2x - 50 = 24$$
$$2x = 74$$
$$x = 37$$

Step4: Solve for y (congruent triangles)

First find $\angle N$: $180 - 142 - 24 = 14^\circ$. Corresponding sides: $NP = SU = 13$
$$2x - y = 13$$
Substitute $x=37$: $2(37) - y = 13$ → $74 - y = 13$ → $y = 61$

Answer:

1. Acute scalene triangle
2. $x = 59$
3. $x = 37$, $y = 61$