{"id":647333,"date":"2023-06-26T22:35:17","date_gmt":"2023-06-26T17:05:17","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-angle-is-18%e2%88%98less-than-its-complementary-angle-what-is-the-measure-of-this-angle\/"},"modified":"2025-06-26T12:41:22","modified_gmt":"2025-06-26T07:11:22","slug":"an-angle-is-18%e2%88%98less-than-its-complementary-angle-what-is-the-measure-of-this-angle","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/an-angle-is-18less-than-its-complementary-angle-what-is-th\/","title":{"rendered":"An angle is 18\u2218less than its complementary angle. What is the measure of this angle?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"An angle is 18\u2218less than its complementary angle. What is the measure of this angle?","custom_permalink":"question\/mathematics\/an-angle-is-18less-than-its-complementary-angle-what-is-th\/"},"categories":[],"acf":{"question":"

An angle is <\/span>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math>less than its complementary angle. What is the measure of this angle?<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"36<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>","correct":true},{"option":"48<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>","correct":false},{"option":"83<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>","correct":false},{"option":"81<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span> <\/span>","correct":false}],"solution":"Given,<\/span>
We have to find an angle is <\/span>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math>less than its complementary angle.<\/span>
Let the smaller angle be x.<\/span>
\u2234<\/mo>Bigger angle<\/mi>=<\/mo> <\/mi>(<\/mo>x<\/mi>+<\/mo>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup>)<\/mo><\/math> <\/span>We know the sum of the complementary angles is<\/span> <\/mi><\/math> <\/span>90<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> .<\/span>
\u21d2<\/mo>x<\/mi>+<\/mo>(<\/mo>x<\/mi>+<\/mo>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup>)<\/mo>=<\/mo>90<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>\u21d2<\/mo>2<\/mn>x<\/mi>=<\/mo>90<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup>-<\/mo>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>\u21d2<\/mo>2<\/mn>x<\/mi>=<\/mo>72<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>\u21d2<\/mo>x<\/mi>=<\/mo>36<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> <\/span>An angle is <\/span>18<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math> less than its complementary angle, then the measure of the angle is <\/span>36<\/mn><\/mrow>\u2218<\/mo><\/mrow><\/msup><\/math>.<\/span>
Therefore, option 1 is correct.<\/span>
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