In ∆ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 16 em and the length of AQ is 4 em, then the length (in cm) CQ is:

In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?

In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?

In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?

In △ABC, BD ⟂ AC at D and ∠DBC = 22°. E is a point on BC such that ∠CAE = 36°. What is the measure of ∠AEB?

In △LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 20 cm and NY = 30 cm, what is the area of △LMN (in cm²)?

The value of x in the given diagram is

In an isosceles triangle, the vertex angle measures 76°. What is the measure of each ofthe base angles?

In $$\triangle$$​PQR, 3 $$\angle$$P = 4$$\angle$$​Q = 6$$\angle$$​R, then find the value of ($$\frac{2 \angle P - \angle Q + 3 \angle R}{5}$$).​