Question 3: Option C: 70
Question 4: Option B: All the angles would become right angles.
Solution:
Question 3:
Sum of all the angles of the triangle = 180°
⇒ 75° + x° + 2x° = 180°
⇒ 75° + 3x° = 180°
Subtract 75° from both sides of the equation.
⇒ 3x° = 105°
Divide by 3 on both sides of the equation.
⇒ x° = 35°
Measure of angle T = 2(35°) = 70°
Option C is the correct answer.
Question 4: m∠4 = 62°
If it increased by 38°, then m∠4 = 62° + 38° = 100°
Option A: The measure of angle 2 would also increase 38°.
∠4 and ∠2 are vertical angles, so they are congruent.
If ∠4 is increased then ∠2 also increased the same.
It is true statement.
Option B: All the angles would become right angles.
It is wrong because m∠4 would become 100°.
It is not true statement.
Option C: The measure of angle 7 would be 80°.
∠4 are ∠3 are supplementary angles.
m∠3 = 180° – 100° = 80°
∠3 and ∠7 are corresponding angles, so they are congruent.
m∠7 = 80°
It is true statement.
Option D: Angle 5 and 6 would be supplementary.
The sum of the adjacent angles in the straight line is 180°.
∠5 and ∠6 are in the straight line, so they are supplementary.
It is true statement.
Hence all the angles would become right angles would not be the correct statement.
