## In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

##### This topic has expert replies
Legendary Member
Posts: 1597
Joined: 01 Mar 2018
Followed by:2 members

### In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

by Gmat_mission » Sun Sep 12, 2021 8:15 am

00:00

A

B

C

D

E

## Global Stats

In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

(1) The measure of $$\angle T$$ is $$100^{\circ}.$$

(2) The measure of $$\angle S$$ is $$40^{\circ}.$$

Source: GMAT Paper Tests

### GMAT/MBA Expert

GMAT Instructor
Posts: 15965
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

### Re: In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

by [email protected] » Sun Sep 12, 2021 9:33 am

00:00

A

B

C

D

E

## Global Stats

Gmat_mission wrote:
Sun Sep 12, 2021 8:15 am
In isosceles triangle $$RST,$$ what is the measure of angle $$R?$$

(1) The measure of $$\angle T$$ is $$100^{\circ}.$$

(2) The measure of $$\angle S$$ is $$40^{\circ}.$$

Source: GMAT Paper Tests
IMPORTANT: In an isosceles triangle there are 2 IDENTICAL angles, and 1 LONE angle.

Target question: What is measure of ∠R?

Statement 1: ∠T = 100 degrees
We should recognize that ∠T CANNOT be one of the identical angles. If this were the case, we'd have two angles with measures of 100 degrees each, which would result in a triangle in which the sum of the angles is GREATER than 180 degree (which is IMPOSSIBLE)
So, we can conclude that ∠T must be the LONE angle, which means ∠R and ∠S are the two IDENTICAL angles.
Since the sum of the 3 angles must be 180, we can conclude that ∠R = 40, ∠S = 40, and ∠T = 100
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ∠S = 40 degrees
Here are two possible cases to consider:
Case a: ∠S is the LONE angle, in which case the ∠R = 70, ∠S = 40, and ∠T = 70
Case b: ∠S is one of the IDENTICAL angles, in which case we could have ∠R = 40, ∠S = 40, and ∠T = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9167759418487549, "perplexity": 1956.7259815863342}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304883.8/warc/CC-MAIN-20220129092458-20220129122458-00572.warc.gz"}