Answer:
90°
Step-by-step explanation:
sum the parts of the ratio 2 + 6 + 8 = 16
The sum of the 3 angles in a triangle = 180°
divide 180 by 16 to find the value of one part of the ratio.
= 11.25° ← 1 part of the ratio
8 parts = 8 × 11.25° = 90°
The largest angle in the triangle is 90°
Answer:
m∠R = 112°
m∠S = 112°
m∠T = 68°
Step-by-step explanation:
Quadrilateral QRST is a cyclic quadrilateral.
A <u>cyclic quadrilateral</u> is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.
The <u>opposite angles</u> in a cyclic quadrilateral sum to 180°.
⇒ m∠Q + m∠S = 180°
⇒ m∠R + m∠T = 180°
Given:
<u>Measure of angle Q</u>
⇒ m∠Q + m∠S = 180°
⇒ 68° + m∠S = 180°
⇒ m∠S = 180° - 68°
⇒ m∠S = 112°
<u>Measure of angles R and T</u>
⇒ m∠R + m∠T = 180°
⇒ (3x + 40)° + (5x - 52)° = 180°
⇒ )8x -12)° = 180°
⇒ 8x° = 192°
⇒ x = 24
Substituting the found value of x into the expressions for angles R and T:
⇒ m∠R = (3(24) + 40)°
⇒ m∠R = 112°
⇒ m∠T = (5x - 52)°
⇒ m∠T = 68°
