Question

In the diagram below, segments RS and RT intersect line m at points T and S, respectively.
Which of these statements is true?

Triangle RST is an isosceles triangle.

Triangle RST is a scalene triangle.

Triangle RST is a right triangle.

Triangle RST is an equilateral triangle.

Answer 1

Answer:

RST is an isosceles triangle

Step-by-step explanation:.

Required

Determine what type of triangle, is RST.

First, we need to determine the angles in RST

Angle on a straight line is 180°.

So, if <mTS = 130°

Then,

<STR = 180° - 130°

<STR = 50°

Similarly,

<TSR = 180° - 130°

<TSR = 50°

The sum of angles in a triangle is 180°.

So:

<TSR + <STR + <TRS = 180°

50 + 50 + <TSR = 180°

100 + <TSR = 180°

<TSR = 180° - 100°

<TSR = 80°

Hence, the three angles of the triangle are: 50°, 50° and 80°

When just two angles of a triangle are equal; such triangle is referred to as an isosceles triangle

Hence, option A answers the question.