Question

4

The diagram below, not drawn to scale, shows two triangles, JLK and MLP, with JK parallel to ML. LM = MP,
KLP is a straight line e JLM = 22° and angle LMP-36°
144
360
Calculate, giving reasons for your answers, the measure of each of the following:
i. ZMLP
ii. ZLJK
iii. LJKL
iv. ZKLJ
​

Answer 1

∠MLP = 72° , ∠LJK = 22° , ∠JKL = 72° , ∠KLJ = 86°

Explanation:

Here, given In ΔJLK and ΔMLP

Here, JK II ML, LM = MP

∠JLM = 22° and ∠LMP = 36°

Now, As angles opposite to equal sides are equal.

⇒ ∠MLP = ∠MPL = x°

Now, in ΔMLP

By ANGLE SUM PROPERTY: ∠MLP + ∠MPL + ∠LMP = 180°

⇒ x° + x° + 36° = 180°

⇒ 2 x = 180 - 36 = 144

or, x = 72°

⇒ ∠MLP = ∠MPL = 72°

Now,as JK II ML

⇒ ∠LJK = ∠JLM = 22° ( Alternate pair of angles)

Now, by the measure of straight angle:

∠MLP + ∠JLM + ∠JLK = 180° ( Straight angle)

⇒ 72° + 22° + ∠JLK = 180°

or, ∠JLK = 86°

In , in ΔJLK

By ANGLE SUM PROPERTY: ∠JKL + ∠JLK + ∠LJK = 180°

⇒ ∠JKL + 86° + 22° = 180°

⇒ ∠JKL = 180 - 108 = 72 , or ∠JKL = 72°

Hence, from above proof , ∠MLP = 72° , ∠LJK = 22° , ∠JKL = 72° ,

∠KLJ = 86°