Question

QHome Spring 2020

Major arc JL measures 300

Which describes triangle JLM?

300

right

obtuse

K

M.

scalene

O equilateral

Answer 1

(D)Equilateral Triangle

Explanation:

Given a circle centre M; and

The measure of major arc JL = 300 degrees

The triangle formed by radii ML and MJ and chord JL is Triangle JLM.

Since ML=MJ (radii of a circle), the base angles are equal.

Therefore:

`\angle MLJ= \angle MJL\\\angle LMJ =60^\circ\\$Therefore:\\\angle LMJ+2\angle MLJ=180^\circ\\60^\circ+2\angle MLJ=180^\circ\\2\angle MLJ=180^\circ-60^\circ\\2\angle MLJ=120^\circ\\\angle MLJ=60^\circ`

We can see that all the angles of triangle JLM are 60 degrees, therefore Triangle JLM is an Equilateral Triangle.