Embibe Experts Solutions for Chapter: Lines and Angles, Exercise 1: Exercise

The figure below is a dish antenna which has signal receiver placed at the focus, $F$. The centre of curvature of the antenna is $C$, and $P$ is the point on the antenna on the same line joining $C$ and $F$. The incoming signals after reflection (The angle of incidence is equal to the angle of reflection), passes through F, where signal receive is placed.

A signal travelling parallel to axis, $CP$ makes an angle of incidence $25°$ $\left(\angle LMC\right)$. 

The measure of $\angle PFM$ is _____ $°$

Two mirrors $AC$ and $AB$ are kept an angle $50°$ with each other. A ray of light falling on $AB$ in parallel to $AC$ suffers reflection at $AB$ and then at $AC$.

The angle of reflection at mirror $AC$ (marked $y$ in the figure) is _____ $°$

Rohan made a shape using matchsticks as shown below, by attaching two legs at the opposite vertices of the square. The angle made by each leg with respect to side of the square is $65°$.  Now Rohan wants to turn the matchstick on the right side so that it is parallel to the one on the left side.

The angle by which Rohan should turn the matchstick on the right side is _____ $°$.

The figure below shows front view of a solar panel fixed on a support, one end of which is firmly grounded at angle of $35°$ and other end is joined with solar panel using a rotatable hinge. The solar panel is fully raised by rotating by the required angle about the hinge on the support so that light rays falls perpendicular on the panel, at a time when sun is $20°$ vertical with the ground.

The measure of angle between the support and solar panel once it is fully raised is _____ $°$

Sita cutout three triangles of different types from a parallelogram $ABCD$ for the purpose of classifying them. $∆ADE$ is an isosceles triangle, $∆AEC$ is an obtuse triangle, $∆ABC$ is an acute triangle. Measure of two angles are marked in the figure.

The measure of angle $\angle CAE$is _____ $°$

Two interstate highways of uniform widths $30 \mathrm{m}$ and $45 \mathrm{m}$ intersect at $55°$ angle as shown below.

What is the measure of angle marked in the figure?

The term, bearing is used to mention the angle relative to the North in clockwise direction. If the bearing is $0°$ it is due North. Similarly $90°, 180°, 270°$ bearing angles are due East, South, and West respectively.

A ship travelled from location $A$ on a bearing $20°$ and on reaching location $B$ it changed its navigation on a bearing $90°$.  When it reached $C$ its bearing changed to $140°$ till it reached location $D.$ Now the ship needs to travel back to its original location, $A$, on a bearing of $280°$. 

What is the measure of $\angle BAD$?