Question

Using a protractor, draw ∠BAC of measure 45°. Take a point P in the interior of ∠BAC. From P draw line segments PM and PN such that PM ⊥ AB and PN ⊥ AC, Measure ∠MPN.

Answer 1

(i) Draw a line segment A on the line l.
(ii) Take a protractor and place it on the segment AC such that AC coincides with the line of the diameter of the protractor and the middle point of the line coincides with point A.
(iii) Counting from the right side, mark a point as B at the point of 45° of protractor and draw a line segment AB.
(iv) Take a convenient radius with P as centre, construct an arc intersecting the line segments AB at T and Q and AC at R and S.
(v) Using the same radius and with T and Q as centres, construct two arcs intersecting at G on the other side.
(vi) Using the same radius and with R and S as centres, construct two arcs intersecting at H on the other side.
(vii) Join PG and PH which intersects AB and AC at M and N, respectively.

On measuring $\angle$MPN using a protractor, we get it equal to 135°.