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=?

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