If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true? Check all that apply.
Answers
Complete Question :- If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true ? Check all that apply.
Statements :-
A) The measure of angle 6 is 20°.
B) The measure of angle 5 is 70°.
C) The measure of angle 2 is 80°.
D) Angles 2 and 5 are complementary.
E) Angles 5 and 6 are supplementary.
F) Angles 1 and 4 are supplementary.
Solution :-
Statement (A) :- The measure of angle 6 is 20°.
given that,
→ ∠3 = (2x + 6)°
→ x = 7
so,
→ ∠3 = (2 * 7 + 6)° = (14 + 6)° = 20°
now,
→ ∠6 = ∠3 (vertically opposite angles.)
→ ∠6 = 20° .
Therefore, statement (A) is True .
Statement (B) :- The measure of angle 5 is 70°.
given that,
→ ∠1 = 90°
so,
→ ∠1 + ∠6 + ∠5 = 180° (Linear pair)
→ 90° + 20° + ∠5 = 180°
→ 110° + ∠5 = 180°
→ ∠5 = 180° - 110°
→ ∠5 = 70° .
Therefore, statement (B) is True .
Statement (C) :- The measure of angle 2 is 80°.
given that,
→ ∠1 = 90°
so,
→ ∠1 + ∠3 + ∠2 = 180° (Linear pair)
→ 90° + 20° + ∠2 = 180°
→ 110° + ∠2 = 180°
→ ∠2 = 180° - 110°
→ ∠2 = 70° .
Therefore, statement (C) is False .
Statement (D) :- Angles 2 and 5 are complementary.
→ ∠2 + ∠5 = 70° + 70°
→ ∠2 + ∠5 = 140° ≠ 90° .
Since, Two angles are called complementary when their measures adds to 90° .
Therefore, statement (D) is False .
Statement (E) :- Angles 5 and 6 are supplementary.
→ ∠5 + ∠6 = 70° + 20°
→ ∠5 + ∠6 = 90° ≠ 180° .
Since, Two angles are called supplementary when their measures adds to 180° .
Therefore, statement (E) is False .
Statement (F) :- Angles 1 and 4 are supplementary.
→ ∠1 = ∠4 (vertically opposite angles.)
so,
→ ∠1 + ∠4 = 90° + 90°
→ ∠1 + ∠4 = 180° .
Since, Two angles are called supplementary when their measures adds to 180° .
Therefore, statement (F) is True .
Learn more :-
In ABC, AD is angle bisector,
angle BAC = 111 and AB+BD=AC find the value of angle ACB=?
https://brainly.in/question/16655884
Answer:
A, B, F
Step-by-step explanation:
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