Subject Experts Solutions for Chapter: Geometry, Exercise 2: PRACTICE QUESTIONS (COMPETITION WING)

In the figure above, $ABCD$ is a parallelogram, and if $AC=14 \mathrm{cm} \mathrm{and} BD=10 \mathrm{cm}$, $AP+BP=$ _____ $\mathrm{cm}$.

The following steps are involved in finding the largest angle of a quadrilateral $PQRS$, if $\angle P:\angle Q:\angle R:\angle S=1:2:3:4$. Arrange them in sequential order.
(A) $10x=360°\Rightarrow x=36°$

(B) Let the angles be $\angle P=x, \angle Q=2x, \angle R=3x \mathrm{and} \angle S=4x$.

(C) The largest angle $=4\left(36°\right)=144°$

(D) Given $\angle P:\angle Q:\angle R:\angle S=1:2:3:4$

(E) $\angle P+\angle Q+\angle R+\angle S=360°\Rightarrow x+2x+3x+4x=360°$

The following steps are involved in finding the third side of an isosceles triangle whose two sides are $6 \mathrm{cm} \mathrm{and} 12 \mathrm{cm}$. Arrange them in sequential order. 
(A) But the difference between two sides is less than the third side.
(B) Since the given triangle is isosceles, the possible measure of the third side is either $6 \mathrm{cm} \mathrm{or} 12 \mathrm{cm}$.
(C) The measure of the third side is $12 \mathrm{cm}$.
(D) $6 \mathrm{cm}$ cannot be the measure of the third side.

The following steps are involved in finding the angles of the triangle $ABC$, when $\angle A:\angle B:\angle C=1:2:3$. Arrange them in sequential order.
(A) Let the angles be $\angle A=x°, \angle B=2x° \mathrm{and} \angle C=3x°$

(B) Given $\angle A:\angle B:\angle C=1:2:3$.

(C) $\angle A=30°, \angle B=2\left(30°\right)=60° \mathrm{and} \angle C=3\left(30°\right)=90°$.

(D) $\angle A+\angle B+\angle C=180°\Rightarrow x°+2x°+3x°=180°$

(E) $6x=180°\Rightarrow x=30°$

The following steps are involved in finding each of interior angle of $10-$sided regular polygon. Arrange them in sequential order.

(A) Each exterior angle $=36°$

(B) Each interior angle $=180°-36°=144°$

(C) Each exterior angle $=\frac{360°}{n}=\frac{360°}{10} (\mathrm{given} n=10)$

In a right triangle, one of the acute angles is four times the other. Find its measure.

In an isosceles triangle $ABC$, $AB=AC \mathrm{and} \angle A=3\angle B$. Find $\angle C$.

The length of two sides of an isosceles triangle are $5 \mathrm{cm} \mathrm{and} 12 \mathrm{cm}$.The length of the third side is